annotate scripts/optimization/sqp.m @ 22755:3a2b891d0b33

maint: Standardize Copyright formatting. * Makefile.am, README, build-aux/check-subst-vars.in.sh, build-aux/find-files-with-tests.sh, build-aux/mk-builtins.sh, build-aux/mk-default-qt-settings.in.sh, build-aux/mk-f77-def.in.sh, build-aux/mk-hg-id.sh, build-aux/mk-mxarray-h.in.sh, build-aux/mk-octave-config-h.sh, build-aux/mk-opts.pl, build-aux/mk-version-h.in.sh, build-aux/subst-config-vals.in.sh, build-aux/subst-cross-config-vals.in.sh, build-aux/subst-default-vals.in.sh, build-aux/subst-f77-isnan-macro.in.sh, build-aux/subst-script-vals.in.sh, configure.ac, doc/interpreter/arith.txi, doc/interpreter/audio.txi, doc/interpreter/basics.txi, doc/interpreter/bugs.txi, doc/interpreter/container.txi, doc/interpreter/cp-idx.txi, doc/interpreter/data.txi, doc/interpreter/debug.txi, doc/interpreter/diagperm.txi, doc/interpreter/diffeq.txi, doc/interpreter/errors.txi, doc/interpreter/eval.txi, doc/interpreter/expr.txi, doc/interpreter/external.txi, doc/interpreter/fn-idx.txi, doc/interpreter/func.txi, doc/interpreter/genpropdoc.m, doc/interpreter/geometry.txi, doc/interpreter/geometryimages.m, doc/interpreter/grammar.txi, doc/interpreter/gui.txi, doc/interpreter/image.txi, doc/interpreter/install.txi, doc/interpreter/interp.txi, doc/interpreter/interpimages.m, doc/interpreter/intro.txi, doc/interpreter/io.txi, doc/interpreter/linalg.txi, doc/interpreter/macros.texi, doc/interpreter/matrix.txi, doc/interpreter/mk-doc-cache.pl, doc/interpreter/mkoctfile.1, doc/interpreter/nonlin.txi, doc/interpreter/numbers.txi, doc/interpreter/obsolete.txi, doc/interpreter/octave-cli.1, doc/interpreter/octave-config.1, doc/interpreter/octave.1, doc/interpreter/octave.css, doc/interpreter/octave.texi, doc/interpreter/oop.txi, doc/interpreter/op-idx.txi, doc/interpreter/optim.txi, doc/interpreter/package.txi, doc/interpreter/plot.txi, doc/interpreter/plotimages.m, doc/interpreter/poly.txi, doc/interpreter/preface.txi, doc/interpreter/quad.txi, doc/interpreter/set.txi, doc/interpreter/signal.txi, doc/interpreter/sparse.txi, doc/interpreter/sparseimages.m, doc/interpreter/splineimages.m, doc/interpreter/stats.txi, doc/interpreter/stmt.txi, doc/interpreter/strings.txi, doc/interpreter/system.txi, doc/interpreter/testfun.txi, doc/interpreter/var.txi, doc/interpreter/vectorize.txi, doc/liboctave/array.texi, doc/liboctave/bugs.texi, doc/liboctave/cp-idx.texi, doc/liboctave/dae.texi, doc/liboctave/diffeq.texi, doc/liboctave/error.texi, doc/liboctave/factor.texi, doc/liboctave/fn-idx.texi, doc/liboctave/gpl.texi, doc/liboctave/install.texi, doc/liboctave/intro.texi, doc/liboctave/liboctave.texi, doc/liboctave/matvec.texi, doc/liboctave/nleqn.texi, doc/liboctave/nlfunc.texi, doc/liboctave/ode.texi, doc/liboctave/optim.texi, doc/liboctave/preface.texi, doc/liboctave/quad.texi, doc/liboctave/range.texi, doc/refcard/refcard-a4.tex, doc/refcard/refcard-legal.tex, doc/refcard/refcard-letter.tex, doc/refcard/refcard.tex, etc/HACKING, etc/icons/octave.appdata.xml.in, libgui/graphics/Backend.cc, libgui/graphics/Backend.h, libgui/graphics/BaseControl.cc, libgui/graphics/BaseControl.h, libgui/graphics/ButtonControl.cc, libgui/graphics/ButtonControl.h, libgui/graphics/ButtonGroup.cc, libgui/graphics/ButtonGroup.h, libgui/graphics/Canvas.cc, libgui/graphics/Canvas.h, libgui/graphics/CheckBoxControl.cc, libgui/graphics/CheckBoxControl.h, libgui/graphics/Container.cc, libgui/graphics/Container.h, libgui/graphics/ContextMenu.cc, libgui/graphics/ContextMenu.h, libgui/graphics/EditControl.cc, libgui/graphics/EditControl.h, libgui/graphics/Figure.cc, libgui/graphics/Figure.h, libgui/graphics/FigureWindow.cc, libgui/graphics/FigureWindow.h, libgui/graphics/GLCanvas.cc, libgui/graphics/GLCanvas.h, libgui/graphics/GenericEventNotify.h, libgui/graphics/KeyMap.cc, libgui/graphics/KeyMap.h, libgui/graphics/ListBoxControl.cc, libgui/graphics/ListBoxControl.h, libgui/graphics/Logger.cc, libgui/graphics/Logger.h, libgui/graphics/Menu.cc, libgui/graphics/Menu.h, libgui/graphics/MenuContainer.h, libgui/graphics/MouseModeActionGroup.cc, libgui/graphics/MouseModeActionGroup.h, libgui/graphics/Object.cc, libgui/graphics/Object.h, libgui/graphics/ObjectFactory.cc, libgui/graphics/ObjectFactory.h, libgui/graphics/ObjectProxy.cc, libgui/graphics/ObjectProxy.h, libgui/graphics/Panel.cc, libgui/graphics/Panel.h, libgui/graphics/PopupMenuControl.cc, libgui/graphics/PopupMenuControl.h, libgui/graphics/PushButtonControl.cc, libgui/graphics/PushButtonControl.h, libgui/graphics/PushTool.cc, libgui/graphics/PushTool.h, libgui/graphics/QtHandlesUtils.cc, libgui/graphics/QtHandlesUtils.h, libgui/graphics/RadioButtonControl.cc, libgui/graphics/RadioButtonControl.h, libgui/graphics/SliderControl.cc, libgui/graphics/SliderControl.h, libgui/graphics/TextControl.cc, libgui/graphics/TextControl.h, libgui/graphics/TextEdit.cc, libgui/graphics/TextEdit.h, libgui/graphics/ToggleButtonControl.cc, libgui/graphics/ToggleButtonControl.h, libgui/graphics/ToggleTool.cc, libgui/graphics/ToggleTool.h, libgui/graphics/ToolBar.cc, libgui/graphics/ToolBar.h, libgui/graphics/ToolBarButton.cc, libgui/graphics/ToolBarButton.h, libgui/graphics/__init_qt__.cc, libgui/graphics/__init_qt__.h, libgui/graphics/annotation-dialog.cc, libgui/graphics/annotation-dialog.h, libgui/graphics/gl-select.cc, libgui/graphics/gl-select.h, libgui/src/color-picker.cc, libgui/src/color-picker.h, libgui/src/dialog.cc, libgui/src/dialog.h, libgui/src/documentation-dock-widget.cc, libgui/src/documentation-dock-widget.h, libgui/src/files-dock-widget.cc, libgui/src/files-dock-widget.h, libgui/src/find-files-dialog.cc, libgui/src/find-files-dialog.h, libgui/src/find-files-model.cc, libgui/src/find-files-model.h, libgui/src/history-dock-widget.cc, libgui/src/history-dock-widget.h, libgui/src/liboctgui-build-info.h, libgui/src/liboctgui-build-info.in.cc, libgui/src/m-editor/file-editor-interface.h, libgui/src/m-editor/file-editor-tab.cc, libgui/src/m-editor/file-editor-tab.h, libgui/src/m-editor/file-editor.cc, libgui/src/m-editor/file-editor.h, libgui/src/m-editor/find-dialog.cc, libgui/src/m-editor/find-dialog.h, libgui/src/m-editor/marker.cc, libgui/src/m-editor/marker.h, libgui/src/m-editor/octave-qscintilla.cc, libgui/src/m-editor/octave-qscintilla.h, libgui/src/m-editor/octave-txt-lexer.cc, libgui/src/m-editor/octave-txt-lexer.h, libgui/src/main-window.cc, libgui/src/main-window.h, libgui/src/octave-cmd.cc, libgui/src/octave-cmd.h, libgui/src/octave-dock-widget.cc, libgui/src/octave-dock-widget.h, libgui/src/octave-gui.cc, libgui/src/octave-gui.h, libgui/src/octave-interpreter.cc, libgui/src/octave-interpreter.h, libgui/src/octave-qt-link.cc, libgui/src/octave-qt-link.h, libgui/src/qtinfo/parser.cc, libgui/src/qtinfo/parser.h, libgui/src/qtinfo/webinfo.cc, libgui/src/qtinfo/webinfo.h, libgui/src/resource-manager.cc, libgui/src/resource-manager.h, libgui/src/settings-dialog.cc, libgui/src/settings-dialog.h, libgui/src/shortcut-manager.cc, libgui/src/shortcut-manager.h, libgui/src/terminal-dock-widget.cc, libgui/src/terminal-dock-widget.h, libgui/src/thread-manager.cc, libgui/src/thread-manager.h, libgui/src/welcome-wizard.cc, libgui/src/welcome-wizard.h, libgui/src/workspace-model.cc, libgui/src/workspace-model.h, libgui/src/workspace-view.cc, libgui/src/workspace-view.h, libinterp/build-env.h, libinterp/build-env.in.cc, libinterp/builtins.h, libinterp/corefcn/Cell.cc, libinterp/corefcn/Cell.h, libinterp/corefcn/__contourc__.cc, libinterp/corefcn/__dsearchn__.cc, libinterp/corefcn/__ichol__.cc, libinterp/corefcn/__ilu__.cc, libinterp/corefcn/__lin_interpn__.cc, libinterp/corefcn/__luinc__.cc, libinterp/corefcn/__magick_read__.cc, libinterp/corefcn/__pchip_deriv__.cc, libinterp/corefcn/__qp__.cc, libinterp/corefcn/balance.cc, libinterp/corefcn/base-text-renderer.h, libinterp/corefcn/besselj.cc, libinterp/corefcn/betainc.cc, libinterp/corefcn/bitfcns.cc, libinterp/corefcn/bsxfun.cc, libinterp/corefcn/c-file-ptr-stream.cc, libinterp/corefcn/c-file-ptr-stream.h, libinterp/corefcn/call-stack.cc, libinterp/corefcn/call-stack.h, libinterp/corefcn/cdisplay.c, libinterp/corefcn/cdisplay.h, libinterp/corefcn/cellfun.cc, libinterp/corefcn/coct-hdf5-types.c, libinterp/corefcn/colloc.cc, libinterp/corefcn/comment-list.cc, libinterp/corefcn/comment-list.h, libinterp/corefcn/conv2.cc, libinterp/corefcn/daspk.cc, libinterp/corefcn/dasrt.cc, libinterp/corefcn/dassl.cc, libinterp/corefcn/data.cc, libinterp/corefcn/data.h, libinterp/corefcn/debug.cc, libinterp/corefcn/debug.h, libinterp/corefcn/defaults.cc, libinterp/corefcn/defaults.in.h, libinterp/corefcn/defun-dld.h, libinterp/corefcn/defun-int.h, libinterp/corefcn/defun.cc, libinterp/corefcn/defun.h, libinterp/corefcn/det.cc, libinterp/corefcn/dirfns.cc, libinterp/corefcn/dirfns.h, libinterp/corefcn/display.cc, libinterp/corefcn/display.h, libinterp/corefcn/dlmread.cc, libinterp/corefcn/dot.cc, libinterp/corefcn/dynamic-ld.cc, libinterp/corefcn/dynamic-ld.h, libinterp/corefcn/eig.cc, libinterp/corefcn/ellipj.cc, libinterp/corefcn/error.cc, libinterp/corefcn/error.h, libinterp/corefcn/errwarn.cc, libinterp/corefcn/errwarn.h, libinterp/corefcn/event-queue.cc, libinterp/corefcn/event-queue.h, libinterp/corefcn/fft.cc, libinterp/corefcn/fft2.cc, libinterp/corefcn/fftn.cc, libinterp/corefcn/file-io.cc, libinterp/corefcn/file-io.h, libinterp/corefcn/filter.cc, libinterp/corefcn/find.cc, libinterp/corefcn/ft-text-renderer.cc, libinterp/corefcn/ft-text-renderer.h, libinterp/corefcn/gammainc.cc, libinterp/corefcn/gcd.cc, libinterp/corefcn/getgrent.cc, libinterp/corefcn/getpwent.cc, libinterp/corefcn/getrusage.cc, libinterp/corefcn/givens.cc, libinterp/corefcn/gl-render.cc, libinterp/corefcn/gl-render.h, libinterp/corefcn/gl2ps-print.cc, libinterp/corefcn/gl2ps-print.h, libinterp/corefcn/graphics.cc, libinterp/corefcn/graphics.in.h, libinterp/corefcn/gripes.cc, libinterp/corefcn/gripes.h, libinterp/corefcn/gsvd.cc, libinterp/corefcn/hash.cc, libinterp/corefcn/help.cc, libinterp/corefcn/help.h, libinterp/corefcn/hess.cc, libinterp/corefcn/hex2num.cc, libinterp/corefcn/hook-fcn.cc, libinterp/corefcn/hook-fcn.h, libinterp/corefcn/input.cc, libinterp/corefcn/input.h, libinterp/corefcn/interpreter.cc, libinterp/corefcn/interpreter.h, libinterp/corefcn/inv.cc, libinterp/corefcn/jit-ir.cc, libinterp/corefcn/jit-ir.h, libinterp/corefcn/jit-typeinfo.cc, libinterp/corefcn/jit-typeinfo.h, libinterp/corefcn/jit-util.cc, libinterp/corefcn/jit-util.h, libinterp/corefcn/kron.cc, libinterp/corefcn/load-path.cc, libinterp/corefcn/load-path.h, libinterp/corefcn/load-save.cc, libinterp/corefcn/load-save.h, libinterp/corefcn/lookup.cc, libinterp/corefcn/ls-ascii-helper.cc, libinterp/corefcn/ls-ascii-helper.h, libinterp/corefcn/ls-hdf5.cc, libinterp/corefcn/ls-hdf5.h, libinterp/corefcn/ls-mat-ascii.cc, libinterp/corefcn/ls-mat-ascii.h, libinterp/corefcn/ls-mat4.cc, libinterp/corefcn/ls-mat4.h, libinterp/corefcn/ls-mat5.cc, libinterp/corefcn/ls-mat5.h, libinterp/corefcn/ls-oct-binary.cc, libinterp/corefcn/ls-oct-binary.h, libinterp/corefcn/ls-oct-text.cc, libinterp/corefcn/ls-oct-text.h, libinterp/corefcn/ls-utils.cc, libinterp/corefcn/ls-utils.h, libinterp/corefcn/lsode.cc, libinterp/corefcn/lu.cc, libinterp/corefcn/mappers.cc, libinterp/corefcn/matrix_type.cc, libinterp/corefcn/max.cc, libinterp/corefcn/mex.cc, libinterp/corefcn/mex.h, libinterp/corefcn/mexproto.h, libinterp/corefcn/mgorth.cc, libinterp/corefcn/mxarray.in.h, libinterp/corefcn/nproc.cc, libinterp/corefcn/oct-errno.h, libinterp/corefcn/oct-errno.in.cc, libinterp/corefcn/oct-fstrm.cc, libinterp/corefcn/oct-fstrm.h, libinterp/corefcn/oct-handle.h, libinterp/corefcn/oct-hdf5-types.cc, libinterp/corefcn/oct-hdf5-types.h, libinterp/corefcn/oct-hdf5.h, libinterp/corefcn/oct-hist.cc, libinterp/corefcn/oct-hist.h, libinterp/corefcn/oct-iostrm.cc, libinterp/corefcn/oct-iostrm.h, libinterp/corefcn/oct-lvalue.cc, libinterp/corefcn/oct-lvalue.h, libinterp/corefcn/oct-map.cc, libinterp/corefcn/oct-map.h, libinterp/corefcn/oct-obj.h, libinterp/corefcn/oct-opengl.h, libinterp/corefcn/oct-prcstrm.cc, libinterp/corefcn/oct-prcstrm.h, libinterp/corefcn/oct-procbuf.cc, libinterp/corefcn/oct-procbuf.h, libinterp/corefcn/oct-stdstrm.h, libinterp/corefcn/oct-stream.cc, libinterp/corefcn/oct-stream.h, libinterp/corefcn/oct-strstrm.cc, libinterp/corefcn/oct-strstrm.h, libinterp/corefcn/oct-tex-lexer.in.ll, libinterp/corefcn/oct-tex-parser.in.yy, libinterp/corefcn/oct.h, libinterp/corefcn/octave-default-image.h, libinterp/corefcn/octave-link.cc, libinterp/corefcn/octave-link.h, libinterp/corefcn/octave-preserve-stream-state.h, libinterp/corefcn/ordschur.cc, libinterp/corefcn/pager.cc, libinterp/corefcn/pager.h, libinterp/corefcn/pinv.cc, libinterp/corefcn/pr-output.cc, libinterp/corefcn/pr-output.h, libinterp/corefcn/procstream.cc, libinterp/corefcn/procstream.h, libinterp/corefcn/profiler.cc, libinterp/corefcn/profiler.h, libinterp/corefcn/psi.cc, libinterp/corefcn/pt-jit.cc, libinterp/corefcn/pt-jit.h, libinterp/corefcn/quad.cc, libinterp/corefcn/quadcc.cc, libinterp/corefcn/qz.cc, libinterp/corefcn/rand.cc, libinterp/corefcn/rcond.cc, libinterp/corefcn/regexp.cc, libinterp/corefcn/schur.cc, libinterp/corefcn/sighandlers.cc, libinterp/corefcn/sighandlers.h, libinterp/corefcn/sparse-xdiv.cc, libinterp/corefcn/sparse-xdiv.h, libinterp/corefcn/sparse-xpow.cc, libinterp/corefcn/sparse-xpow.h, libinterp/corefcn/sparse.cc, libinterp/corefcn/spparms.cc, libinterp/corefcn/sqrtm.cc, libinterp/corefcn/str2double.cc, libinterp/corefcn/strfind.cc, libinterp/corefcn/strfns.cc, libinterp/corefcn/sub2ind.cc, libinterp/corefcn/svd.cc, libinterp/corefcn/sylvester.cc, libinterp/corefcn/symtab.cc, libinterp/corefcn/symtab.h, libinterp/corefcn/syscalls.cc, libinterp/corefcn/sysdep.cc, libinterp/corefcn/sysdep.h, libinterp/corefcn/text-renderer.cc, libinterp/corefcn/text-renderer.h, libinterp/corefcn/time.cc, libinterp/corefcn/toplev.cc, libinterp/corefcn/toplev.h, libinterp/corefcn/tril.cc, libinterp/corefcn/tsearch.cc, libinterp/corefcn/txt-eng.cc, libinterp/corefcn/txt-eng.h, libinterp/corefcn/typecast.cc, libinterp/corefcn/urlwrite.cc, libinterp/corefcn/utils.cc, libinterp/corefcn/utils.h, libinterp/corefcn/variables.cc, libinterp/corefcn/variables.h, libinterp/corefcn/workspace-element.h, libinterp/corefcn/xdiv.cc, libinterp/corefcn/xdiv.h, libinterp/corefcn/xnorm.cc, libinterp/corefcn/xnorm.h, libinterp/corefcn/xpow.cc, libinterp/corefcn/xpow.h, libinterp/corefcn/zfstream.cc, libinterp/corefcn/zfstream.h, libinterp/deprecated-config.h, libinterp/dldfcn/__delaunayn__.cc, libinterp/dldfcn/__eigs__.cc, libinterp/dldfcn/__fltk_uigetfile__.cc, libinterp/dldfcn/__glpk__.cc, libinterp/dldfcn/__init_fltk__.cc, libinterp/dldfcn/__init_gnuplot__.cc, libinterp/dldfcn/__osmesa_print__.cc, libinterp/dldfcn/__voronoi__.cc, libinterp/dldfcn/amd.cc, libinterp/dldfcn/audiodevinfo.cc, libinterp/dldfcn/audioread.cc, libinterp/dldfcn/ccolamd.cc, libinterp/dldfcn/chol.cc, libinterp/dldfcn/colamd.cc, libinterp/dldfcn/convhulln.cc, libinterp/dldfcn/dmperm.cc, libinterp/dldfcn/fftw.cc, libinterp/dldfcn/gzip.cc, libinterp/dldfcn/oct-qhull.h, libinterp/dldfcn/qr.cc, libinterp/dldfcn/symbfact.cc, libinterp/dldfcn/symrcm.cc, libinterp/gendoc.pl, libinterp/genprops.awk, libinterp/liboctinterp-build-info.h, libinterp/liboctinterp-build-info.in.cc, libinterp/mk-errno-list, libinterp/mk-pkg-add, libinterp/mkops, libinterp/octave-value/ov-base-diag.cc, libinterp/octave-value/ov-base-diag.h, libinterp/octave-value/ov-base-int.cc, libinterp/octave-value/ov-base-int.h, libinterp/octave-value/ov-base-mat.cc, libinterp/octave-value/ov-base-mat.h, libinterp/octave-value/ov-base-scalar.cc, libinterp/octave-value/ov-base-scalar.h, libinterp/octave-value/ov-base-sparse.cc, libinterp/octave-value/ov-base-sparse.h, libinterp/octave-value/ov-base.cc, libinterp/octave-value/ov-base.h, libinterp/octave-value/ov-bool-mat.cc, libinterp/octave-value/ov-bool-mat.h, libinterp/octave-value/ov-bool-sparse.cc, libinterp/octave-value/ov-bool-sparse.h, libinterp/octave-value/ov-bool.cc, libinterp/octave-value/ov-bool.h, libinterp/octave-value/ov-builtin.cc, libinterp/octave-value/ov-builtin.h, libinterp/octave-value/ov-cell.cc, libinterp/octave-value/ov-cell.h, libinterp/octave-value/ov-ch-mat.cc, libinterp/octave-value/ov-ch-mat.h, libinterp/octave-value/ov-class.cc, libinterp/octave-value/ov-class.h, libinterp/octave-value/ov-classdef.cc, libinterp/octave-value/ov-classdef.h, libinterp/octave-value/ov-colon.cc, libinterp/octave-value/ov-colon.h, libinterp/octave-value/ov-complex.cc, libinterp/octave-value/ov-complex.h, libinterp/octave-value/ov-cs-list.cc, libinterp/octave-value/ov-cs-list.h, libinterp/octave-value/ov-cx-diag.cc, libinterp/octave-value/ov-cx-diag.h, libinterp/octave-value/ov-cx-mat.cc, libinterp/octave-value/ov-cx-mat.h, libinterp/octave-value/ov-cx-sparse.cc, libinterp/octave-value/ov-cx-sparse.h, libinterp/octave-value/ov-dld-fcn.cc, libinterp/octave-value/ov-dld-fcn.h, libinterp/octave-value/ov-fcn-handle.cc, libinterp/octave-value/ov-fcn-handle.h, libinterp/octave-value/ov-fcn-inline.cc, libinterp/octave-value/ov-fcn-inline.h, libinterp/octave-value/ov-fcn.cc, libinterp/octave-value/ov-fcn.h, libinterp/octave-value/ov-float.cc, libinterp/octave-value/ov-float.h, libinterp/octave-value/ov-flt-complex.cc, libinterp/octave-value/ov-flt-complex.h, libinterp/octave-value/ov-flt-cx-diag.cc, libinterp/octave-value/ov-flt-cx-diag.h, libinterp/octave-value/ov-flt-cx-mat.cc, libinterp/octave-value/ov-flt-cx-mat.h, libinterp/octave-value/ov-flt-re-diag.cc, libinterp/octave-value/ov-flt-re-diag.h, libinterp/octave-value/ov-flt-re-mat.cc, libinterp/octave-value/ov-flt-re-mat.h, libinterp/octave-value/ov-int-traits.h, libinterp/octave-value/ov-int16.cc, libinterp/octave-value/ov-int16.h, libinterp/octave-value/ov-int32.cc, libinterp/octave-value/ov-int32.h, libinterp/octave-value/ov-int64.cc, libinterp/octave-value/ov-int64.h, libinterp/octave-value/ov-int8.cc, libinterp/octave-value/ov-int8.h, libinterp/octave-value/ov-intx.h, libinterp/octave-value/ov-java.cc, libinterp/octave-value/ov-java.h, libinterp/octave-value/ov-lazy-idx.cc, libinterp/octave-value/ov-lazy-idx.h, libinterp/octave-value/ov-mex-fcn.cc, libinterp/octave-value/ov-mex-fcn.h, libinterp/octave-value/ov-null-mat.cc, libinterp/octave-value/ov-null-mat.h, libinterp/octave-value/ov-oncleanup.cc, libinterp/octave-value/ov-oncleanup.h, libinterp/octave-value/ov-perm.cc, libinterp/octave-value/ov-perm.h, libinterp/octave-value/ov-range.cc, libinterp/octave-value/ov-range.h, libinterp/octave-value/ov-re-diag.cc, libinterp/octave-value/ov-re-diag.h, libinterp/octave-value/ov-re-mat.cc, libinterp/octave-value/ov-re-mat.h, libinterp/octave-value/ov-re-sparse.cc, libinterp/octave-value/ov-re-sparse.h, libinterp/octave-value/ov-scalar.cc, libinterp/octave-value/ov-scalar.h, libinterp/octave-value/ov-str-mat.cc, libinterp/octave-value/ov-str-mat.h, libinterp/octave-value/ov-struct.cc, libinterp/octave-value/ov-struct.h, libinterp/octave-value/ov-typeinfo.cc, libinterp/octave-value/ov-typeinfo.h, libinterp/octave-value/ov-uint16.cc, libinterp/octave-value/ov-uint16.h, libinterp/octave-value/ov-uint32.cc, libinterp/octave-value/ov-uint32.h, libinterp/octave-value/ov-uint64.cc, libinterp/octave-value/ov-uint64.h, libinterp/octave-value/ov-uint8.cc, libinterp/octave-value/ov-uint8.h, libinterp/octave-value/ov-usr-fcn.cc, libinterp/octave-value/ov-usr-fcn.h, libinterp/octave-value/ov.cc, libinterp/octave-value/ov.h, libinterp/octave-value/ovl.cc, libinterp/octave-value/ovl.h, libinterp/octave.cc, libinterp/octave.h, libinterp/op-kw-docs, libinterp/operators/op-b-b.cc, libinterp/operators/op-b-bm.cc, libinterp/operators/op-b-sbm.cc, libinterp/operators/op-bm-b.cc, libinterp/operators/op-bm-bm.cc, libinterp/operators/op-bm-sbm.cc, libinterp/operators/op-cdm-cdm.cc, libinterp/operators/op-cdm-cm.cc, libinterp/operators/op-cdm-cs.cc, libinterp/operators/op-cdm-dm.cc, libinterp/operators/op-cdm-m.cc, libinterp/operators/op-cdm-s.cc, libinterp/operators/op-cell.cc, libinterp/operators/op-chm.cc, libinterp/operators/op-class.cc, libinterp/operators/op-cm-cdm.cc, libinterp/operators/op-cm-cm.cc, libinterp/operators/op-cm-cs.cc, libinterp/operators/op-cm-dm.cc, libinterp/operators/op-cm-m.cc, libinterp/operators/op-cm-pm.cc, libinterp/operators/op-cm-s.cc, libinterp/operators/op-cm-scm.cc, libinterp/operators/op-cm-sm.cc, libinterp/operators/op-cs-cm.cc, libinterp/operators/op-cs-cs.cc, libinterp/operators/op-cs-m.cc, libinterp/operators/op-cs-s.cc, libinterp/operators/op-cs-scm.cc, libinterp/operators/op-cs-sm.cc, libinterp/operators/op-dm-cdm.cc, libinterp/operators/op-dm-cm.cc, libinterp/operators/op-dm-cs.cc, libinterp/operators/op-dm-dm.cc, libinterp/operators/op-dm-m.cc, libinterp/operators/op-dm-s.cc, libinterp/operators/op-dm-scm.cc, libinterp/operators/op-dm-sm.cc, libinterp/operators/op-dm-template.cc, libinterp/operators/op-dms-template.cc, libinterp/operators/op-fcdm-fcdm.cc, libinterp/operators/op-fcdm-fcm.cc, libinterp/operators/op-fcdm-fcs.cc, libinterp/operators/op-fcdm-fdm.cc, libinterp/operators/op-fcdm-fm.cc, libinterp/operators/op-fcdm-fs.cc, libinterp/operators/op-fcm-fcdm.cc, libinterp/operators/op-fcm-fcm.cc, libinterp/operators/op-fcm-fcs.cc, libinterp/operators/op-fcm-fdm.cc, libinterp/operators/op-fcm-fm.cc, libinterp/operators/op-fcm-fs.cc, libinterp/operators/op-fcm-pm.cc, libinterp/operators/op-fcn.cc, libinterp/operators/op-fcs-fcm.cc, libinterp/operators/op-fcs-fcs.cc, libinterp/operators/op-fcs-fm.cc, libinterp/operators/op-fcs-fs.cc, libinterp/operators/op-fdm-fcdm.cc, libinterp/operators/op-fdm-fcm.cc, libinterp/operators/op-fdm-fcs.cc, libinterp/operators/op-fdm-fdm.cc, libinterp/operators/op-fdm-fm.cc, libinterp/operators/op-fdm-fs.cc, libinterp/operators/op-fm-fcdm.cc, libinterp/operators/op-fm-fcm.cc, libinterp/operators/op-fm-fcs.cc, libinterp/operators/op-fm-fdm.cc, libinterp/operators/op-fm-fm.cc, libinterp/operators/op-fm-fs.cc, libinterp/operators/op-fm-pm.cc, libinterp/operators/op-fs-fcm.cc, libinterp/operators/op-fs-fcs.cc, libinterp/operators/op-fs-fm.cc, libinterp/operators/op-fs-fs.cc, libinterp/operators/op-i16-i16.cc, libinterp/operators/op-i32-i32.cc, libinterp/operators/op-i64-i64.cc, libinterp/operators/op-i8-i8.cc, libinterp/operators/op-int-concat.cc, libinterp/operators/op-int.h, libinterp/operators/op-m-cdm.cc, libinterp/operators/op-m-cm.cc, libinterp/operators/op-m-cs.cc, libinterp/operators/op-m-dm.cc, libinterp/operators/op-m-m.cc, libinterp/operators/op-m-pm.cc, libinterp/operators/op-m-s.cc, libinterp/operators/op-m-scm.cc, libinterp/operators/op-m-sm.cc, libinterp/operators/op-pm-cm.cc, libinterp/operators/op-pm-fcm.cc, libinterp/operators/op-pm-fm.cc, libinterp/operators/op-pm-m.cc, libinterp/operators/op-pm-pm.cc, libinterp/operators/op-pm-scm.cc, libinterp/operators/op-pm-sm.cc, libinterp/operators/op-pm-template.cc, libinterp/operators/op-range.cc, libinterp/operators/op-s-cm.cc, libinterp/operators/op-s-cs.cc, libinterp/operators/op-s-m.cc, libinterp/operators/op-s-s.cc, libinterp/operators/op-s-scm.cc, libinterp/operators/op-s-sm.cc, libinterp/operators/op-sbm-b.cc, libinterp/operators/op-sbm-bm.cc, libinterp/operators/op-sbm-sbm.cc, libinterp/operators/op-scm-cm.cc, libinterp/operators/op-scm-cs.cc, libinterp/operators/op-scm-m.cc, libinterp/operators/op-scm-s.cc, libinterp/operators/op-scm-scm.cc, libinterp/operators/op-scm-sm.cc, libinterp/operators/op-sm-cm.cc, libinterp/operators/op-sm-cs.cc, libinterp/operators/op-sm-m.cc, libinterp/operators/op-sm-s.cc, libinterp/operators/op-sm-scm.cc, libinterp/operators/op-sm-sm.cc, libinterp/operators/op-str-m.cc, libinterp/operators/op-str-s.cc, libinterp/operators/op-str-str.cc, libinterp/operators/op-struct.cc, libinterp/operators/op-ui16-ui16.cc, libinterp/operators/op-ui32-ui32.cc, libinterp/operators/op-ui64-ui64.cc, libinterp/operators/op-ui8-ui8.cc, libinterp/operators/ops.h, libinterp/options-usage.h, libinterp/parse-tree/lex.h, libinterp/parse-tree/lex.ll, libinterp/parse-tree/oct-parse.in.yy, libinterp/parse-tree/octave.gperf, libinterp/parse-tree/parse.h, libinterp/parse-tree/pt-all.h, libinterp/parse-tree/pt-arg-list.cc, libinterp/parse-tree/pt-arg-list.h, libinterp/parse-tree/pt-array-list.cc, libinterp/parse-tree/pt-array-list.h, libinterp/parse-tree/pt-assign.cc, libinterp/parse-tree/pt-assign.h, libinterp/parse-tree/pt-binop.cc, libinterp/parse-tree/pt-binop.h, libinterp/parse-tree/pt-bp.cc, libinterp/parse-tree/pt-bp.h, libinterp/parse-tree/pt-cbinop.cc, libinterp/parse-tree/pt-cbinop.h, libinterp/parse-tree/pt-cell.cc, libinterp/parse-tree/pt-cell.h, libinterp/parse-tree/pt-check.cc, libinterp/parse-tree/pt-check.h, libinterp/parse-tree/pt-classdef.cc, libinterp/parse-tree/pt-classdef.h, libinterp/parse-tree/pt-cmd.cc, libinterp/parse-tree/pt-cmd.h, libinterp/parse-tree/pt-colon.cc, libinterp/parse-tree/pt-colon.h, libinterp/parse-tree/pt-const.cc, libinterp/parse-tree/pt-const.h, libinterp/parse-tree/pt-decl.cc, libinterp/parse-tree/pt-decl.h, libinterp/parse-tree/pt-eval.cc, libinterp/parse-tree/pt-eval.h, libinterp/parse-tree/pt-except.cc, libinterp/parse-tree/pt-except.h, libinterp/parse-tree/pt-exp.cc, libinterp/parse-tree/pt-exp.h, libinterp/parse-tree/pt-fcn-handle.cc, libinterp/parse-tree/pt-fcn-handle.h, libinterp/parse-tree/pt-funcall.cc, libinterp/parse-tree/pt-funcall.h, libinterp/parse-tree/pt-id.cc, libinterp/parse-tree/pt-id.h, libinterp/parse-tree/pt-idx.cc, libinterp/parse-tree/pt-idx.h, libinterp/parse-tree/pt-jump.cc, libinterp/parse-tree/pt-jump.h, libinterp/parse-tree/pt-loop.cc, libinterp/parse-tree/pt-loop.h, libinterp/parse-tree/pt-mat.cc, libinterp/parse-tree/pt-mat.h, libinterp/parse-tree/pt-misc.cc, libinterp/parse-tree/pt-misc.h, libinterp/parse-tree/pt-pr-code.cc, libinterp/parse-tree/pt-pr-code.h, libinterp/parse-tree/pt-select.cc, libinterp/parse-tree/pt-select.h, libinterp/parse-tree/pt-stmt.cc, libinterp/parse-tree/pt-stmt.h, libinterp/parse-tree/pt-unop.cc, libinterp/parse-tree/pt-unop.h, libinterp/parse-tree/pt-walk.h, libinterp/parse-tree/pt.cc, libinterp/parse-tree/pt.h, libinterp/parse-tree/token.cc, libinterp/parse-tree/token.h, libinterp/template-inst/Array-jit.cc, libinterp/template-inst/Array-tc.cc, libinterp/version.cc, libinterp/version.in.h, liboctave/array/Array-C.cc, liboctave/array/Array-b.cc, liboctave/array/Array-ch.cc, liboctave/array/Array-d.cc, liboctave/array/Array-f.cc, liboctave/array/Array-fC.cc, liboctave/array/Array-i.cc, liboctave/array/Array-idx-vec.cc, liboctave/array/Array-s.cc, liboctave/array/Array-str.cc, liboctave/array/Array-util.cc, liboctave/array/Array-util.h, liboctave/array/Array-voidp.cc, liboctave/array/Array.cc, liboctave/array/Array.h, liboctave/array/CColVector.cc, liboctave/array/CColVector.h, liboctave/array/CDiagMatrix.cc, liboctave/array/CDiagMatrix.h, liboctave/array/CMatrix.cc, liboctave/array/CMatrix.h, liboctave/array/CNDArray.cc, liboctave/array/CNDArray.h, liboctave/array/CRowVector.cc, liboctave/array/CRowVector.h, liboctave/array/CSparse.cc, liboctave/array/CSparse.h, liboctave/array/DiagArray2.cc, liboctave/array/DiagArray2.h, liboctave/array/MArray-C.cc, liboctave/array/MArray-d.cc, liboctave/array/MArray-f.cc, liboctave/array/MArray-fC.cc, liboctave/array/MArray-i.cc, liboctave/array/MArray-s.cc, liboctave/array/MArray.cc, liboctave/array/MArray.h, liboctave/array/MDiagArray2.cc, liboctave/array/MDiagArray2.h, liboctave/array/MSparse-C.cc, liboctave/array/MSparse-d.cc, liboctave/array/MSparse.cc, liboctave/array/MSparse.h, liboctave/array/Matrix.h, liboctave/array/MatrixType.cc, liboctave/array/MatrixType.h, liboctave/array/PermMatrix.cc, liboctave/array/PermMatrix.h, liboctave/array/Range.cc, liboctave/array/Range.h, liboctave/array/Sparse-C.cc, liboctave/array/Sparse-b.cc, liboctave/array/Sparse-d.cc, liboctave/array/Sparse.cc, liboctave/array/Sparse.h, liboctave/array/boolMatrix.cc, liboctave/array/boolMatrix.h, liboctave/array/boolNDArray.cc, liboctave/array/boolNDArray.h, liboctave/array/boolSparse.cc, liboctave/array/boolSparse.h, liboctave/array/chMatrix.cc, liboctave/array/chMatrix.h, liboctave/array/chNDArray.cc, liboctave/array/chNDArray.h, liboctave/array/dColVector.cc, liboctave/array/dColVector.h, liboctave/array/dDiagMatrix.cc, liboctave/array/dDiagMatrix.h, liboctave/array/dMatrix.cc, liboctave/array/dMatrix.h, liboctave/array/dNDArray.cc, liboctave/array/dNDArray.h, liboctave/array/dRowVector.cc, liboctave/array/dRowVector.h, liboctave/array/dSparse.cc, liboctave/array/dSparse.h, liboctave/array/dim-vector.cc, liboctave/array/dim-vector.h, liboctave/array/fCColVector.cc, liboctave/array/fCColVector.h, liboctave/array/fCDiagMatrix.cc, liboctave/array/fCDiagMatrix.h, liboctave/array/fCMatrix.cc, liboctave/array/fCMatrix.h, liboctave/array/fCNDArray.cc, liboctave/array/fCNDArray.h, liboctave/array/fCRowVector.cc, liboctave/array/fCRowVector.h, liboctave/array/fColVector.cc, liboctave/array/fColVector.h, liboctave/array/fDiagMatrix.cc, liboctave/array/fDiagMatrix.h, liboctave/array/fMatrix.cc, liboctave/array/fMatrix.h, liboctave/array/fNDArray.cc, liboctave/array/fNDArray.h, liboctave/array/fRowVector.cc, liboctave/array/fRowVector.h, liboctave/array/idx-vector.cc, liboctave/array/idx-vector.h, liboctave/array/int16NDArray.cc, liboctave/array/int16NDArray.h, liboctave/array/int32NDArray.cc, liboctave/array/int32NDArray.h, liboctave/array/int64NDArray.cc, liboctave/array/int64NDArray.h, liboctave/array/int8NDArray.cc, liboctave/array/int8NDArray.h, liboctave/array/intNDArray.cc, liboctave/array/intNDArray.h, liboctave/array/uint16NDArray.cc, liboctave/array/uint16NDArray.h, liboctave/array/uint32NDArray.cc, liboctave/array/uint32NDArray.h, liboctave/array/uint64NDArray.cc, liboctave/array/uint64NDArray.h, liboctave/array/uint8NDArray.cc, liboctave/array/uint8NDArray.h, liboctave/cruft/misc/blaswrap.c, liboctave/cruft/misc/cquit.c, liboctave/cruft/misc/f77-extern.cc, liboctave/cruft/misc/f77-fcn.c, liboctave/cruft/misc/f77-fcn.h, liboctave/cruft/misc/lo-error.c, liboctave/cruft/misc/lo-error.h, liboctave/cruft/misc/quit.cc, liboctave/cruft/misc/quit.h, liboctave/liboctave-build-info.h, liboctave/liboctave-build-info.in.cc, liboctave/numeric/CollocWt.cc, liboctave/numeric/CollocWt.h, liboctave/numeric/DAE.h, liboctave/numeric/DAEFunc.h, liboctave/numeric/DAERT.h, liboctave/numeric/DAERTFunc.h, liboctave/numeric/DASPK-opts.in, liboctave/numeric/DASPK.cc, liboctave/numeric/DASPK.h, liboctave/numeric/DASRT-opts.in, liboctave/numeric/DASRT.cc, liboctave/numeric/DASRT.h, liboctave/numeric/DASSL-opts.in, liboctave/numeric/DASSL.cc, liboctave/numeric/DASSL.h, liboctave/numeric/DET.h, liboctave/numeric/EIG.cc, liboctave/numeric/EIG.h, liboctave/numeric/LSODE-opts.in, liboctave/numeric/LSODE.cc, liboctave/numeric/LSODE.h, liboctave/numeric/ODE.h, liboctave/numeric/ODEFunc.h, liboctave/numeric/ODES.cc, liboctave/numeric/ODES.h, liboctave/numeric/ODESFunc.h, liboctave/numeric/Quad-opts.in, liboctave/numeric/Quad.cc, liboctave/numeric/Quad.h, liboctave/numeric/aepbalance.cc, liboctave/numeric/aepbalance.h, liboctave/numeric/base-dae.h, liboctave/numeric/base-de.h, liboctave/numeric/base-min.h, liboctave/numeric/bsxfun-decl.h, liboctave/numeric/bsxfun-defs.cc, liboctave/numeric/bsxfun.h, liboctave/numeric/chol.cc, liboctave/numeric/chol.h, liboctave/numeric/eigs-base.cc, liboctave/numeric/eigs-base.h, liboctave/numeric/fEIG.cc, liboctave/numeric/fEIG.h, liboctave/numeric/gepbalance.cc, liboctave/numeric/gepbalance.h, liboctave/numeric/gsvd.cc, liboctave/numeric/gsvd.h, liboctave/numeric/hess.cc, liboctave/numeric/hess.h, liboctave/numeric/lo-amos-proto.h, liboctave/numeric/lo-arpack-proto.h, liboctave/numeric/lo-blas-proto.h, liboctave/numeric/lo-fftpack-proto.h, liboctave/numeric/lo-lapack-proto.h, liboctave/numeric/lo-mappers.cc, liboctave/numeric/lo-mappers.h, liboctave/numeric/lo-qrupdate-proto.h, liboctave/numeric/lo-ranlib-proto.h, liboctave/numeric/lo-slatec-proto.h, liboctave/numeric/lo-specfun.cc, liboctave/numeric/lo-specfun.h, liboctave/numeric/lu.cc, liboctave/numeric/lu.h, liboctave/numeric/oct-convn.cc, liboctave/numeric/oct-convn.h, liboctave/numeric/oct-fftw.cc, liboctave/numeric/oct-fftw.h, liboctave/numeric/oct-norm.cc, liboctave/numeric/oct-norm.h, liboctave/numeric/oct-rand.cc, liboctave/numeric/oct-rand.h, liboctave/numeric/oct-spparms.cc, liboctave/numeric/oct-spparms.h, liboctave/numeric/qr.cc, liboctave/numeric/qr.h, liboctave/numeric/qrp.cc, liboctave/numeric/qrp.h, liboctave/numeric/randgamma.cc, liboctave/numeric/randgamma.h, liboctave/numeric/randmtzig.cc, liboctave/numeric/randmtzig.h, liboctave/numeric/randpoisson.cc, liboctave/numeric/randpoisson.h, liboctave/numeric/schur.cc, liboctave/numeric/schur.h, liboctave/numeric/sparse-chol.cc, liboctave/numeric/sparse-chol.h, liboctave/numeric/sparse-dmsolve.cc, liboctave/numeric/sparse-dmsolve.h, liboctave/numeric/sparse-lu.cc, liboctave/numeric/sparse-lu.h, liboctave/numeric/sparse-qr.cc, liboctave/numeric/sparse-qr.h, liboctave/numeric/svd.cc, liboctave/numeric/svd.h, liboctave/operators/Sparse-diag-op-defs.h, liboctave/operators/Sparse-op-decls.h, liboctave/operators/Sparse-op-defs.h, liboctave/operators/Sparse-perm-op-defs.h, liboctave/operators/mk-ops.awk, liboctave/operators/mx-base.h, liboctave/operators/mx-defs.h, liboctave/operators/mx-ext.h, 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test/classdef/classdef.tst, test/classes/classes.tst, test/colormaps.tst, test/complex.tst, test/ctor-vs-method/ctor-vs-method.tst, test/diag-perm.tst, test/error.tst, test/eval-catch.tst, test/fcn-handle-derived-resolution/fcn-handle-derived-resolution.tst, test/fntests.m, test/for.tst, test/func.tst, test/global.tst, test/if.tst, test/index.tst, test/io.tst, test/jit.tst, test/line-continue.tst, test/logical-index.tst, test/nest/nest.tst, test/null-assign.tst, test/parser.tst, test/prefer.tst, test/range.tst, test/recursion.tst, test/return.tst, test/slice.tst, test/struct.tst, test/switch.tst, test/system.tst, test/transpose.tst, test/try.tst, test/unwind.tst, test/while.tst: Use the same Copyright formatting throughout Octave.
author Rik <rik@octave.org>
date Sun, 13 Nov 2016 20:33:47 -0800
parents bac0d6f07a3e
children ef4d915df748
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1 ## Copyright (C) 2005-2016 John W. Eaton
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2 ## Copyright (C) 2013-2016 Arun Giridhar
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3 ##
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4 ## This file is part of Octave.
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5 ##
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6 ## Octave is free software; you can redistribute it and/or modify it
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7 ## under the terms of the GNU General Public License as published by
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8 ## the Free Software Foundation; either version 3 of the License, or
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9 ## (at your option) any later version.
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10 ##
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11 ## Octave is distributed in the hope that it will be useful, but
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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14 ## GNU General Public License for more details.
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15 ##
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16 ## You should have received a copy of the GNU General Public License
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17 ## along with Octave; see the file COPYING. If not, see
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18 ## <http://www.gnu.org/licenses/>.
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19
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20 ## -*- texinfo -*-
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21 ## @deftypefn {} {[@var{x}, @var{obj}, @var{info}, @var{iter}, @var{nf}, @var{lambda}] =} sqp (@var{x0}, @var{phi})
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22 ## @deftypefnx {} {[@dots{}] =} sqp (@var{x0}, @var{phi}, @var{g})
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23 ## @deftypefnx {} {[@dots{}] =} sqp (@var{x0}, @var{phi}, @var{g}, @var{h})
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24 ## @deftypefnx {} {[@dots{}] =} sqp (@var{x0}, @var{phi}, @var{g}, @var{h}, @var{lb}, @var{ub})
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25 ## @deftypefnx {} {[@dots{}] =} sqp (@var{x0}, @var{phi}, @var{g}, @var{h}, @var{lb}, @var{ub}, @var{maxiter})
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26 ## @deftypefnx {} {[@dots{}] =} sqp (@var{x0}, @var{phi}, @var{g}, @var{h}, @var{lb}, @var{ub}, @var{maxiter}, @var{tol})
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27 ## Minimize an objective function using sequential quadratic programming (SQP).
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28 ##
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29 ## Solve the nonlinear program
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30 ## @tex
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31 ## $$
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32 ## \min_x \phi (x)
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33 ## $$
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34 ## @end tex
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35 ## @ifnottex
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36 ##
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37 ## @example
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38 ## @group
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39 ## min phi (x)
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40 ## x
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41 ## @end group
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42 ## @end example
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43 ##
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44 ## @end ifnottex
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45 ## subject to
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46 ## @tex
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47 ## $$
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48 ## g(x) = 0 \qquad h(x) \geq 0 \qquad lb \leq x \leq ub
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49 ## $$
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50 ## @end tex
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51 ## @ifnottex
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52 ##
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53 ## @example
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54 ## @group
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55 ## g(x) = 0
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56 ## h(x) >= 0
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57 ## lb <= x <= ub
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58 ## @end group
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59 ## @end example
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60 ##
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61 ## @end ifnottex
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62 ## @noindent
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63 ## using a sequential quadratic programming method.
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64 ##
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65 ## The first argument is the initial guess for the vector @var{x0}.
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66 ##
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67 ## The second argument is a function handle pointing to the objective function
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68 ## @var{phi}. The objective function must accept one vector argument and
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69 ## return a scalar.
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70 ##
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71 ## The second argument may also be a 2- or 3-element cell array of function
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72 ## handles. The first element should point to the objective function, the
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73 ## second should point to a function that computes the gradient of the
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74 ## objective function, and the third should point to a function that computes
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75 ## the Hessian of the objective function. If the gradient function is not
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76 ## supplied, the gradient is computed by finite differences. If the Hessian
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77 ## function is not supplied, a BFGS update formula is used to approximate the
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78 ## Hessian.
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79 ##
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80 ## When supplied, the gradient function @code{@var{phi}@{2@}} must accept one
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81 ## vector argument and return a vector. When supplied, the Hessian function
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82 ## @code{@var{phi}@{3@}} must accept one vector argument and return a matrix.
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83 ##
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84 ## The third and fourth arguments @var{g} and @var{h} are function handles
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85 ## pointing to functions that compute the equality constraints and the
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86 ## inequality constraints, respectively. If the problem does not have
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87 ## equality (or inequality) constraints, then use an empty matrix ([]) for
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88 ## @var{g} (or @var{h}). When supplied, these equality and inequality
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89 ## constraint functions must accept one vector argument and return a vector.
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90 ##
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91 ## The third and fourth arguments may also be 2-element cell arrays of
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92 ## function handles. The first element should point to the constraint
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93 ## function and the second should point to a function that computes the
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94 ## gradient of the constraint function:
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95 ## @tex
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96 ## $$
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97 ## \Bigg( {\partial f(x) \over \partial x_1},
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98 ## {\partial f(x) \over \partial x_2}, \ldots,
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99 ## {\partial f(x) \over \partial x_N} \Bigg)^T
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100 ## $$
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101 ## @end tex
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102 ## @ifnottex
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103 ##
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104 ## @example
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105 ## @group
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106 ## [ d f(x) d f(x) d f(x) ]
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107 ## transpose ( [ ------ ----- ... ------ ] )
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108 ## [ dx_1 dx_2 dx_N ]
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109 ## @end group
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110 ## @end example
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111 ##
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112 ## @end ifnottex
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113 ## The fifth and sixth arguments, @var{lb} and @var{ub}, contain lower and
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114 ## upper bounds on @var{x}. These must be consistent with the equality and
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115 ## inequality constraints @var{g} and @var{h}. If the arguments are vectors
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116 ## then @var{x}(i) is bound by @var{lb}(i) and @var{ub}(i). A bound can also
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117 ## be a scalar in which case all elements of @var{x} will share the same
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118 ## bound. If only one bound (lb, ub) is specified then the other will
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119 ## default to (-@var{realmax}, +@var{realmax}).
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120 ##
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121 ## The seventh argument @var{maxiter} specifies the maximum number of
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122 ## iterations. The default value is 100.
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123 ##
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124 ## The eighth argument @var{tol} specifies the tolerance for the stopping
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125 ## criteria. The default value is @code{sqrt (eps)}.
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126 ##
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127 ## The value returned in @var{info} may be one of the following:
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128 ##
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129 ## @table @asis
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130 ## @item 101
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131 ## The algorithm terminated normally.
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132 ## All constraints meet the specified tolerance.
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133 ##
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134 ## @item 102
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135 ## The BFGS update failed.
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136 ##
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137 ## @item 103
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138 ## The maximum number of iterations was reached.
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139 ##
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140 ## @item 104
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141 ## The stepsize has become too small, i.e.,
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142 ## @tex
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143 ## $\Delta x,$
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144 ## @end tex
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145 ## @ifnottex
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146 ## delta @var{x},
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147 ## @end ifnottex
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148 ## is less than @code{@var{tol} * norm (x)}.
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149 ## @end table
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150 ##
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151 ## An example of calling @code{sqp}:
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152 ##
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153 ## @example
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154 ## function r = g (x)
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155 ## r = [ sumsq(x)-10;
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156 ## x(2)*x(3)-5*x(4)*x(5);
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157 ## x(1)^3+x(2)^3+1 ];
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158 ## endfunction
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159 ##
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160 ## function obj = phi (x)
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161 ## obj = exp (prod (x)) - 0.5*(x(1)^3+x(2)^3+1)^2;
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162 ## endfunction
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163 ##
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164 ## x0 = [-1.8; 1.7; 1.9; -0.8; -0.8];
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165 ##
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166 ## [x, obj, info, iter, nf, lambda] = sqp (x0, @@phi, @@g, [])
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167 ##
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168 ## x =
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169 ##
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170 ## -1.71714
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171 ## 1.59571
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172 ## 1.82725
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173 ## -0.76364
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174 ## -0.76364
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175 ##
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176 ## obj = 0.053950
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177 ## info = 101
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178 ## iter = 8
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179 ## nf = 10
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180 ## lambda =
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181 ##
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182 ## -0.0401627
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183 ## 0.0379578
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184 ## -0.0052227
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185 ## @end example
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186 ##
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187 ## @seealso{qp}
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188 ## @end deftypefn
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189
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190 function [x, obj, info, iter, nf, lambda] = sqp (x0, objf, cef, cif, lb, ub, maxiter, tolerance)
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191
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192 globals = struct (); # data and handles, needed and changed by subfunctions
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193
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194 if (nargin < 2 || nargin > 8 || nargin == 5)
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195 print_usage ();
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196 endif
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197
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198 if (! isvector (x0))
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199 error ("sqp: X0 must be a vector");
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200 endif
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201 if (rows (x0) == 1)
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202 x0 = x0';
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203 endif
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204
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205 have_hess = 0;
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206 if (iscell (objf))
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207 switch (numel (objf))
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208 case 1
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209 obj_fun = objf{1};
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210 obj_grd = @(x) fd_obj_grd (x, obj_fun);
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211 case 2
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212 obj_fun = objf{1};
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213 obj_grd = objf{2};
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214 case 3
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215 obj_fun = objf{1};
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216 obj_grd = objf{2};
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217 obj_hess = objf{3};
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218 have_hess = 1;
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219 otherwise
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220 error ("sqp: invalid objective function specification");
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221 endswitch
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222 else
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223 obj_fun = objf; # No cell array, only obj_fun set
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224 obj_grd = @(x) fd_obj_grd (x, obj_fun);
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225 endif
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226
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227 ce_fun = @empty_cf;
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228 ce_grd = @empty_jac;
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229 if (nargin > 2)
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230 if (iscell (cef))
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231 switch (numel (cef))
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232 case 1
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233 ce_fun = cef{1};
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234 ce_grd = @(x) fd_ce_jac (x, ce_fun);
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235 case 2
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236 ce_fun = cef{1};
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237 ce_grd = cef{2};
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238 otherwise
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239 error ("sqp: invalid equality constraint function specification");
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240 endswitch
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241 elseif (! isempty (cef))
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242 ce_fun = cef; # No cell array, only constraint equality function set
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243 ce_grd = @(x) fd_ce_jac (x, ce_fun);
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244 endif
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245 endif
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246
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247 ci_fun = @empty_cf;
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248 ci_grd = @empty_jac;
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249 if (nargin > 3)
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250 ## constraint function given by user with possible gradient
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251 globals.cif = cif;
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252 ## constraint function given by user without gradient
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253 globals.cifcn = @empty_cf;
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254 if (iscell (cif))
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255 if (length (cif) > 0)
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256 globals.cifcn = cif{1};
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257 endif
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258 elseif (! isempty (cif))
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259 globals.cifcn = cif;
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260 endif
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261
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262 if (nargin < 5 || (nargin > 5 && isempty (lb) && isempty (ub)))
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263 ## constraint inequality function only without any bounds
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264 ci_grd = @(x) fd_ci_jac (x, globals.cifcn);
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265 if (iscell (cif))
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266 switch (length (cif))
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267 case 1
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268 ci_fun = cif{1};
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269 case 2
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270 ci_fun = cif{1};
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271 ci_grd = cif{2};
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272 otherwise
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273 error ("sqp: invalid inequality constraint function specification");
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274 endswitch
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275 elseif (! isempty (cif))
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276 ci_fun = cif; # No cell array, only constraint inequality function set
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277 endif
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278 else
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279 ## constraint inequality function with bounds present
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280 lb_idx = ub_idx = true (size (x0));
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diff changeset
281 ub_grad = - (lb_grad = eye (rows (x0)));
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282 if (isvector (lb))
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diff changeset
283 globals.lb = tmp_lb = lb(:);
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284 lb_idx(:) = tmp_idx = (lb != -Inf);
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diff changeset
285 globals.lb = globals.lb(tmp_idx, 1);
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diff changeset
286 lb_grad = lb_grad(lb_idx, :);
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diff changeset
287 elseif (isempty (lb))
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288 if (isa (x0, "single"))
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diff changeset
289 globals.lb = tmp_lb = -realmax ("single");
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290 else
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diff changeset
291 globals.lb = tmp_lb = -realmax;
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diff changeset
292 endif
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
293 else
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
294 error ("sqp: invalid lower bound");
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
295 endif
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
296
10678
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Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
297 if (isvector (ub))
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
298 globals.ub = tmp_ub = ub(:);
11347
2726132f77f6 sqp.m: Remove never violated Inf bounds from computation (bug #31742)
Rik <octave@nomad.inbox5.com>
parents: 11290
diff changeset
299 ub_idx(:) = tmp_idx = (ub != Inf);
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
300 globals.ub = globals.ub(tmp_idx, 1);
11347
2726132f77f6 sqp.m: Remove never violated Inf bounds from computation (bug #31742)
Rik <octave@nomad.inbox5.com>
parents: 11290
diff changeset
301 ub_grad = ub_grad(ub_idx, :);
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
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parents: 10549
diff changeset
302 elseif (isempty (ub))
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
303 if (isa (x0, "single"))
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
304 globals.ub = tmp_ub = realmax ("single");
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
305 else
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
306 globals.ub = tmp_ub = realmax;
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10542
diff changeset
307 endif
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
308 else
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
309 error ("sqp: invalid upper bound");
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
310 endif
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
311
11347
2726132f77f6 sqp.m: Remove never violated Inf bounds from computation (bug #31742)
Rik <octave@nomad.inbox5.com>
parents: 11290
diff changeset
312 if (any (tmp_lb > tmp_ub))
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
313 error ("sqp: upper bound smaller than lower bound");
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
314 endif
11347
2726132f77f6 sqp.m: Remove never violated Inf bounds from computation (bug #31742)
Rik <octave@nomad.inbox5.com>
parents: 11290
diff changeset
315 bounds_grad = [lb_grad; ub_grad];
19833
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 19697
diff changeset
316 ci_fun = @(x) cf_ub_lb (x, lb_idx, ub_idx, globals);
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 19697
diff changeset
317 ci_grd = @(x) cigrad_ub_lb (x, bounds_grad, globals);
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
318 endif
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
319
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
320 endif # if (nargin > 3)
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
321
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
322 iter_max = 100;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
323 if (nargin > 6 && ! isempty (maxiter))
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
324 if (isscalar (maxiter) && maxiter > 0 && fix (maxiter) == maxiter)
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
325 iter_max = maxiter;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
326 else
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
327 error ("sqp: invalid number of maximum iterations");
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
328 endif
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
329 endif
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
330
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
331 tol = sqrt (eps);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
332 if (nargin > 7 && ! isempty (tolerance))
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
333 if (isscalar (tolerance) && tolerance > 0)
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
334 tol = tolerance;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
335 else
11472
1740012184f9 Use uppercase for variable names in error() strings to match Info documentation. Only m-files done.
Rik <octave@nomad.inbox5.com>
parents: 11371
diff changeset
336 error ("sqp: invalid value for TOLERANCE");
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
337 endif
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
338 endif
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
339
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
340 ## Initialize variables for search loop
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
341 ## Seed x with initial guess and evaluate objective function, constraints,
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
342 ## and gradients at initial value x0.
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
343 ##
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
344 ## obj_fun -- objective function
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
345 ## obj_grad -- objective gradient
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
346 ## ce_fun -- equality constraint functions
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
347 ## ci_fun -- inequality constraint functions
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
348 ## A == [grad_{x_1} cx_fun, grad_{x_2} cx_fun, ..., grad_{x_n} cx_fun]^T
11587
c792872f8942 all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
349 x = x0;
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
350
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
351 obj = feval (obj_fun, x0);
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
352 globals.nfun = 1;
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
353
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
354 c = feval (obj_grd, x0);
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
355
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
356 ## Choose an initial NxN symmetric positive definite Hessian approximation B.
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
357 n = length (x0);
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
358 if (have_hess)
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
359 B = feval (obj_hess, x0);
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
360 else
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
361 B = eye (n, n);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
362 endif
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
363
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
364 ce = feval (ce_fun, x0);
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
365 F = feval (ce_grd, x0);
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
366
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
367 ci = feval (ci_fun, x0);
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
368 C = feval (ci_grd, x0);
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
369
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
370 A = [F; C];
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
371
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
372 ## Choose an initial lambda (x is provided by the caller).
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
373 lambda = 100 * ones (rows (A), 1);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
374
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
375 qp_iter = 1;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
376 alpha = 1;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
377
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
378 info = 0;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
379 iter = 0;
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
380 # report (); # Called with no arguments to initialize reporting
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
381 # report (iter, qp_iter, alpha, __sqp_nfun__, obj);
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
382
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
383 while (++iter < iter_max)
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
384
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
385 ## Check convergence. This is just a simple check on the first
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
386 ## order necessary conditions.
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
387 nr_f = rows (F);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
388
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
389 lambda_e = lambda((1:nr_f)');
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
390 lambda_i = lambda((nr_f+1:end)');
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
391
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
392 con = [ce; ci];
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
393
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
394 t0 = norm (c - A' * lambda);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
395 t1 = norm (ce);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
396 t2 = all (ci >= 0);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
397 t3 = all (lambda_i >= 0);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
398 t4 = norm (lambda .* con);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
399
18255
f58a6cd3f909 sqp.m: Fix return values in sqp (bug #32008).
Arun Giridhar <arungiridhar@gmail.com>
parents: 17744
diff changeset
400 ## Normal convergence. All constraints are satisfied
f58a6cd3f909 sqp.m: Fix return values in sqp (bug #32008).
Arun Giridhar <arungiridhar@gmail.com>
parents: 17744
diff changeset
401 ## and objective has converged.
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
402 if (t2 && t3 && max ([t0; t1; t4]) < tol)
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
403 info = 101;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
404 break;
6382
f74e71ef6612 [project @ 2007-03-05 21:29:40 by jwe]
jwe
parents: 6046
diff changeset
405 endif
f74e71ef6612 [project @ 2007-03-05 21:29:40 by jwe]
jwe
parents: 6046
diff changeset
406
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
407 ## Compute search direction p by solving QP.
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
408 g = -ce;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
409 d = -ci;
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
410
22224
20e0c0b8820c Allow sequential quadratic programs with infeasible QPs (bug #36015).
Lachlan Andrew <lachlanbis@gmail.com>
parents: 21758
diff changeset
411 old_lambda = lambda;
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
412 [p, obj_qp, INFO, lambda] = qp (x, B, c, F, g, [], [], d, C,
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
413 Inf (size (d)));
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
414
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
415 info = INFO.info;
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
416
18255
f58a6cd3f909 sqp.m: Fix return values in sqp (bug #32008).
Arun Giridhar <arungiridhar@gmail.com>
parents: 17744
diff changeset
417 ## FIXME: check QP solution and attempt to recover if it has failed.
f58a6cd3f909 sqp.m: Fix return values in sqp (bug #32008).
Arun Giridhar <arungiridhar@gmail.com>
parents: 17744
diff changeset
418 ## For now, just warn about possible problems.
19593
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 17744
diff changeset
419
13206
658aa9fd8665 sqp: provide warnings for QP subproblem failures
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
420 id = "Octave:SQP-QP-subproblem";
658aa9fd8665 sqp: provide warnings for QP subproblem failures
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
421 switch (info)
658aa9fd8665 sqp: provide warnings for QP subproblem failures
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
422 case 2
658aa9fd8665 sqp: provide warnings for QP subproblem failures
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
423 warning (id, "sqp: QP subproblem is non-convex and unbounded");
658aa9fd8665 sqp: provide warnings for QP subproblem failures
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
424 case 3
658aa9fd8665 sqp: provide warnings for QP subproblem failures
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
425 warning (id, "sqp: QP subproblem failed to converge in %d iterations",
658aa9fd8665 sqp: provide warnings for QP subproblem failures
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
426 INFO.solveiter);
658aa9fd8665 sqp: provide warnings for QP subproblem failures
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
427 case 6
658aa9fd8665 sqp: provide warnings for QP subproblem failures
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
428 warning (id, "sqp: QP subproblem is infeasible");
22224
20e0c0b8820c Allow sequential quadratic programs with infeasible QPs (bug #36015).
Lachlan Andrew <lachlanbis@gmail.com>
parents: 21758
diff changeset
429 lambda = old_lambda; # The return value was size 0x0 in this case.
13206
658aa9fd8665 sqp: provide warnings for QP subproblem failures
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
430 endswitch
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
431
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
432 ## Choose mu such that p is a descent direction for the chosen
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
433 ## merit function phi.
17245
7babcdb9bc13 Use ... instead of \ for line continuation marker.
Stefan Mahr <dac922@gmx.de>
parents: 17174
diff changeset
434 [x_new, alpha, obj_new, globals] = ...
7babcdb9bc13 Use ... instead of \ for line continuation marker.
Stefan Mahr <dac922@gmx.de>
parents: 17174
diff changeset
435 linesearch_L1 (x, p, obj_fun, obj_grd, ce_fun, ci_fun, lambda, ...
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
436 obj, globals);
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
437
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
438 ## Evaluate objective function, constraints, and gradients at x_new.
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
439 c_new = feval (obj_grd, x_new);
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
440
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
441 ce_new = feval (ce_fun, x_new);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
442 F_new = feval (ce_grd, x_new);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
443
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
444 ci_new = feval (ci_fun, x_new);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
445 C_new = feval (ci_grd, x_new);
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
446
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
447 A_new = [F_new; C_new];
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
448
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
449 ## Set
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
450 ##
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
451 ## s = alpha * p
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
452 ## y = grad_x L (x_new, lambda) - grad_x L (x, lambda})
6527
2a04f026ef54 [project @ 2007-04-16 16:54:09 by jwe]
jwe
parents: 6382
diff changeset
453
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
454 y = c_new - c;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
455
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
456 if (! isempty (A))
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
457 t = ((A_new - A)'*lambda);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
458 y -= t;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
459 endif
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
460
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
461 delx = x_new - x;
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
462
18255
f58a6cd3f909 sqp.m: Fix return values in sqp (bug #32008).
Arun Giridhar <arungiridhar@gmail.com>
parents: 17744
diff changeset
463 ## Check if step size has become too small (indicates lack of progress).
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
464 if (norm (delx) < tol * norm (x))
18255
f58a6cd3f909 sqp.m: Fix return values in sqp (bug #32008).
Arun Giridhar <arungiridhar@gmail.com>
parents: 17744
diff changeset
465 info = 104;
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
466 break;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
467 endif
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
468
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
469 if (have_hess)
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
470
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
471 B = feval (obj_hess, x);
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
472
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
473 else
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
474 ## Update B using a quasi-Newton formula.
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
475 delxt = delx';
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
476
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
477 ## Damped BFGS. Or maybe we would actually want to use the Hessian
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
478 ## of the Lagrangian, computed directly?
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
479 d1 = delxt*B*delx;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
480
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
481 t1 = 0.2 * d1;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
482 t2 = delxt*y;
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
483
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
484 if (t2 < t1)
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
485 theta = 0.8*d1/(d1 - t2);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
486 else
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
487 theta = 1;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
488 endif
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
489
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
490 r = theta*y + (1-theta)*B*delx;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
491
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
492 d2 = delxt*r;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
493
18255
f58a6cd3f909 sqp.m: Fix return values in sqp (bug #32008).
Arun Giridhar <arungiridhar@gmail.com>
parents: 17744
diff changeset
494 ## Check if the next BFGS update will work properly.
f58a6cd3f909 sqp.m: Fix return values in sqp (bug #32008).
Arun Giridhar <arungiridhar@gmail.com>
parents: 17744
diff changeset
495 ## If d1 or d2 vanish, the BFGS update will fail.
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
496 if (d1 == 0 || d2 == 0)
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
497 info = 102;
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10542
diff changeset
498 break;
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
499 endif
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
500
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
501 B = B - B*delx*delxt*B/d1 + r*r'/d2;
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
502
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
503 endif
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
504
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
505 x = x_new;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
506
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
507 obj = obj_new;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
508
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
509 c = c_new;
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
510
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
511 ce = ce_new;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
512 F = F_new;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
513
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
514 ci = ci_new;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
515 C = C_new;
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
516
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
517 A = A_new;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
518
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
519 # report (iter, qp_iter, alpha, __sqp_nfun__, obj);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
520
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
521 endwhile
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
522
18255
f58a6cd3f909 sqp.m: Fix return values in sqp (bug #32008).
Arun Giridhar <arungiridhar@gmail.com>
parents: 17744
diff changeset
523 ## Check if we've spent too many iterations without converging.
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
524 if (iter >= iter_max)
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
525 info = 103;
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
526 endif
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
527
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
528 nf = globals.nfun;
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
529
7399
c1a3d6c7d2fb [project @ 2008-01-18 07:37:35 by jwe]
jwe
parents: 7381
diff changeset
530 endfunction
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
531
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
532
17245
7babcdb9bc13 Use ... instead of \ for line continuation marker.
Stefan Mahr <dac922@gmx.de>
parents: 17174
diff changeset
533 function [merit, obj, globals] = phi_L1 (obj, obj_fun, ce_fun, ci_fun, ...
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
534 x, mu, globals)
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
535
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
536 ce = feval (ce_fun, x);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
537 ci = feval (ci_fun, x);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
538
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
539 idx = ci < 0;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
540
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
541 con = [ce; ci(idx)];
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
542
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
543 if (isempty (obj))
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
544 obj = feval (obj_fun, x);
20735
418ae0cb752f Replace ++,-- with in-place operators for performance.
Rik <rik@octave.org>
parents: 20165
diff changeset
545 globals.nfun += 1;
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
546 endif
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
547
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
548 merit = obj;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
549 t = norm (con, 1) / mu;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
550
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
551 if (! isempty (t))
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
552 merit += t;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
553 endif
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
554
7399
c1a3d6c7d2fb [project @ 2008-01-18 07:37:35 by jwe]
jwe
parents: 7381
diff changeset
555 endfunction
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
556
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
557
17245
7babcdb9bc13 Use ... instead of \ for line continuation marker.
Stefan Mahr <dac922@gmx.de>
parents: 17174
diff changeset
558 function [x_new, alpha, obj, globals] = ...
21758
ffad2baa90f7 maint: Use newlines to make code more readable.
Rik <rik@octave.org>
parents: 21634
diff changeset
559 linesearch_L1 (x, p, obj_fun, obj_grd, ce_fun, ci_fun, lambda, obj, globals)
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
560
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
561 ## Choose parameters
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
562 ##
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
563 ## eta in the range (0, 0.5)
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
564 ## tau in the range (0, 1)
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
565
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
566 eta = 0.25;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
567 tau = 0.5;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
568
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
569 delta_bar = sqrt (eps);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
570
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
571 if (isempty (lambda))
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
572 mu = 1 / delta_bar;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
573 else
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
574 mu = 1 / (norm (lambda, Inf) + delta_bar);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
575 endif
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
576
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
577 alpha = 1;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
578
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
579 c = feval (obj_grd, x);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
580 ce = feval (ce_fun, x);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
581
17245
7babcdb9bc13 Use ... instead of \ for line continuation marker.
Stefan Mahr <dac922@gmx.de>
parents: 17174
diff changeset
582 [phi_x_mu, obj, globals] = phi_L1 (obj, obj_fun, ce_fun, ci_fun, x, ...
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
583 mu, globals);
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
584
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
585 D_phi_x_mu = c' * p;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
586 d = feval (ci_fun, x);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
587 ## only those elements of d corresponding
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
588 ## to violated constraints should be included.
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
589 idx = d < 0;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
590 t = - norm ([ce; d(idx)], 1) / mu;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
591 if (! isempty (t))
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
592 D_phi_x_mu += t;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
593 endif
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
594
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
595 while (1)
17245
7babcdb9bc13 Use ... instead of \ for line continuation marker.
Stefan Mahr <dac922@gmx.de>
parents: 17174
diff changeset
596 [p1, obj, globals] = phi_L1 ([], obj_fun, ce_fun, ci_fun, ...
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
597 x+alpha*p, mu, globals);
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
598 p2 = phi_x_mu+eta*alpha*D_phi_x_mu;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
599 if (p1 > p2)
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
600 ## Reset alpha = tau_alpha * alpha for some tau_alpha in the
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
601 ## range (0, tau).
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
602 tau_alpha = 0.9 * tau; # ??
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
603 alpha = tau_alpha * alpha;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
604 else
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
605 break;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
606 endif
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
607 endwhile
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
608
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
609 x_new = x + alpha * p;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
610
7399
c1a3d6c7d2fb [project @ 2008-01-18 07:37:35 by jwe]
jwe
parents: 7381
diff changeset
611 endfunction
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
612
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
613
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
614 function grd = fdgrd (f, x)
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
615
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
616 if (! isempty (f))
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
617 y0 = feval (f, x);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
618 nx = length (x);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
619 grd = zeros (nx, 1);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
620 deltax = sqrt (eps);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
621 for i = 1:nx
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
622 t = x(i);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
623 x(i) += deltax;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
624 grd(i) = (feval (f, x) - y0) / deltax;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
625 x(i) = t;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
626 endfor
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
627 else
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
628 grd = zeros (0, 1);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
629 endif
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
630
7399
c1a3d6c7d2fb [project @ 2008-01-18 07:37:35 by jwe]
jwe
parents: 7381
diff changeset
631 endfunction
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
632
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
633
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
634 function jac = fdjac (f, x)
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
635
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
636 nx = length (x);
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
637 if (! isempty (f))
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
638 y0 = feval (f, x);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
639 nf = length (y0);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
640 nx = length (x);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
641 jac = zeros (nf, nx);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
642 deltax = sqrt (eps);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
643 for i = 1:nx
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
644 t = x(i);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
645 x(i) += deltax;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
646 jac(:,i) = (feval (f, x) - y0) / deltax;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
647 x(i) = t;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
648 endfor
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
649 else
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
650 jac = zeros (0, nx);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
651 endif
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
652
7399
c1a3d6c7d2fb [project @ 2008-01-18 07:37:35 by jwe]
jwe
parents: 7381
diff changeset
653 endfunction
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
654
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
655
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
656 function grd = fd_obj_grd (x, obj_fun)
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
657
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
658 grd = fdgrd (obj_fun, x);
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
659
7399
c1a3d6c7d2fb [project @ 2008-01-18 07:37:35 by jwe]
jwe
parents: 7381
diff changeset
660 endfunction
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
661
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
662
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
663 function res = empty_cf (x)
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
664
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
665 res = zeros (0, 1);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
666
7399
c1a3d6c7d2fb [project @ 2008-01-18 07:37:35 by jwe]
jwe
parents: 7381
diff changeset
667 endfunction
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
668
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
669
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
670 function res = empty_jac (x)
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
671
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
672 res = zeros (0, length (x));
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
673
7399
c1a3d6c7d2fb [project @ 2008-01-18 07:37:35 by jwe]
jwe
parents: 7381
diff changeset
674 endfunction
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
675
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
676
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
677 function jac = fd_ce_jac (x, ce_fun)
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
678
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
679 jac = fdjac (ce_fun, x);
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
680
7399
c1a3d6c7d2fb [project @ 2008-01-18 07:37:35 by jwe]
jwe
parents: 7381
diff changeset
681 endfunction
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
682
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
683
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
684 function jac = fd_ci_jac (x, cifcn)
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
685
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
686 ## cifcn = constraint function without gradients and lb or ub
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
687 jac = fdjac (cifcn, x);
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
688
7399
c1a3d6c7d2fb [project @ 2008-01-18 07:37:35 by jwe]
jwe
parents: 7381
diff changeset
689 endfunction
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
690
7017
a1dbe9d80eee [project @ 2007-10-12 21:27:11 by jwe]
jwe
parents: 7016
diff changeset
691
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
692 function res = cf_ub_lb (x, lbidx, ubidx, globals)
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
693
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
694 ## combine constraint function with ub and lb
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
695 if (isempty (globals.cifcn))
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
696 res = [x(lbidx,1)-globals.lb; globals.ub-x(ubidx,1)];
11347
2726132f77f6 sqp.m: Remove never violated Inf bounds from computation (bug #31742)
Rik <octave@nomad.inbox5.com>
parents: 11290
diff changeset
697 else
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
698 res = [feval(globals.cifcn,x); x(lbidx,1)-globals.lb;
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
699 globals.ub-x(ubidx,1)];
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
700 endif
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
701
7399
c1a3d6c7d2fb [project @ 2008-01-18 07:37:35 by jwe]
jwe
parents: 7381
diff changeset
702 endfunction
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
703
7017
a1dbe9d80eee [project @ 2007-10-12 21:27:11 by jwe]
jwe
parents: 7016
diff changeset
704
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
705 function res = cigrad_ub_lb (x, bgrad, globals)
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
706
19833
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 19697
diff changeset
707 cigradfcn = @(x) fd_ci_jac (x, globals.cifcn);
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
708
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
709 if (iscell (globals.cif) && length (globals.cif) > 1)
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
710 cigradfcn = globals.cif{2};
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
711 endif
11587
c792872f8942 all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
712
11347
2726132f77f6 sqp.m: Remove never violated Inf bounds from computation (bug #31742)
Rik <octave@nomad.inbox5.com>
parents: 11290
diff changeset
713 if (isempty (cigradfcn))
2726132f77f6 sqp.m: Remove never violated Inf bounds from computation (bug #31742)
Rik <octave@nomad.inbox5.com>
parents: 11290
diff changeset
714 res = bgrad;
2726132f77f6 sqp.m: Remove never violated Inf bounds from computation (bug #31742)
Rik <octave@nomad.inbox5.com>
parents: 11290
diff changeset
715 else
2726132f77f6 sqp.m: Remove never violated Inf bounds from computation (bug #31742)
Rik <octave@nomad.inbox5.com>
parents: 11290
diff changeset
716 res = [feval(cigradfcn,x); bgrad];
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
717 endif
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
718
7399
c1a3d6c7d2fb [project @ 2008-01-18 07:37:35 by jwe]
jwe
parents: 7381
diff changeset
719 endfunction
7361
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
720
19833
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 19697
diff changeset
721 ## Utility function used to debug sqp
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
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parents: 11347
diff changeset
722 function report (iter, qp_iter, alpha, nfun, obj)
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
723
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
724 if (nargin == 0)
21634
96518f623c91 Backed out changeset dcf8922b724b
Mike Miller <mtmiller@octave.org>
parents: 21633
diff changeset
725 printf (" Itn ItQP Step Nfun Objective\n");
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2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
726 else
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96518f623c91 Backed out changeset dcf8922b724b
Mike Miller <mtmiller@octave.org>
parents: 21633
diff changeset
727 printf ("%5d %4d %8.1g %5d %13.6e\n", iter, qp_iter, alpha, nfun, obj);
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
728 endif
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
729
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
730 endfunction
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
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parents: 11347
diff changeset
731
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
732
19833
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 19697
diff changeset
733 ################################################################################
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 19697
diff changeset
734 ## Test Code
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
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parents: 11347
diff changeset
735
13305
63463570d9fe Add %!endfunction block keyword to test.m
Rik <octave@nomad.inbox5.com>
parents: 13268
diff changeset
736 %!function r = __g (x)
7371
fe9a44d753d6 [project @ 2008-01-14 19:34:22 by jwe]
jwe
parents: 7361
diff changeset
737 %! r = [sumsq(x)-10;
fe9a44d753d6 [project @ 2008-01-14 19:34:22 by jwe]
jwe
parents: 7361
diff changeset
738 %! x(2)*x(3)-5*x(4)*x(5);
fe9a44d753d6 [project @ 2008-01-14 19:34:22 by jwe]
jwe
parents: 7361
diff changeset
739 %! x(1)^3+x(2)^3+1 ];
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Rik <octave@nomad.inbox5.com>
parents: 13268
diff changeset
740 %!endfunction
7361
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
741 %!
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parents: 13268
diff changeset
742 %!function obj = __phi (x)
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f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
743 %! obj = exp (prod (x)) - 0.5*(x(1)^3 + x(2)^3 + 1)^2;
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63463570d9fe Add %!endfunction block keyword to test.m
Rik <octave@nomad.inbox5.com>
parents: 13268
diff changeset
744 %!endfunction
7361
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
745 %!
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
746 %!test
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Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
747 %!
7361
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
748 %! x0 = [-1.8; 1.7; 1.9; -0.8; -0.8];
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
749 %!
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Rik <octave@nomad.inbox5.com>
parents: 13268
diff changeset
750 %! [x, obj, info, iter, nf, lambda] = sqp (x0, @__phi, @__g, []);
7361
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
751 %!
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
752 %! x_opt = [-1.717143501952599;
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
753 %! 1.595709610928535;
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
754 %! 1.827245880097156;
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
755 %! -0.763643103133572;
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
756 %! -0.763643068453300];
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
757 %!
7371
fe9a44d753d6 [project @ 2008-01-14 19:34:22 by jwe]
jwe
parents: 7361
diff changeset
758 %! obj_opt = 0.0539498477702739;
7361
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
759 %!
15757
534a2c881f45 Increase test tolerance on sqp (bug #37742)
Mike Miller <mtmiller@ieee.org>
parents: 14868
diff changeset
760 %! assert (x, x_opt, 8*sqrt (eps));
14363
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Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
761 %! assert (obj, obj_opt, sqrt (eps));
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Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
762
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Rik <rik@octave.org>
parents: 19697
diff changeset
763 ## Test input validation
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Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
764 %!error sqp ()
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
765 %!error sqp (1)
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
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parents: 10549
diff changeset
766 %!error sqp (1,2,3,4,5,6,7,8,9)
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
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parents: 10549
diff changeset
767 %!error sqp (1,2,3,4,5)
14363
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parents: 14327
diff changeset
768 %!error sqp (ones (2,2))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
769 %!error sqp (1, cell (4,1))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
770 %!error sqp (1, cell (3,1), cell (3,1))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
771 %!error sqp (1, cell (3,1), cell (2,1), cell (3,1))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
772 %!error sqp (1, cell (3,1), cell (2,1), cell (2,1), ones (2,2),[])
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
773 %!error sqp (1, cell (3,1), cell (2,1), cell (2,1),[], ones (2,2))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
774 %!error sqp (1, cell (3,1), cell (2,1), cell (2,1),1,-1)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
775 %!error sqp (1, cell (3,1), cell (2,1), cell (2,1),[],[], ones (2,2))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
776 %!error sqp (1, cell (3,1), cell (2,1), cell (2,1),[],[],-1)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
777 %!error sqp (1, cell (3,1), cell (2,1), cell (2,1),[],[],1.5)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
778 %!error sqp (1, cell (3,1), cell (2,1), cell (2,1),[],[],[], ones (2,2))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
779 %!error sqp (1, cell (3,1), cell (2,1), cell (2,1),[],[],[],-1)
17338
1c89599167a6 maint: End m-files with 1 blank line.
Rik <rik@octave.org>
parents: 17336
diff changeset
780