Mercurial > octave
annotate scripts/optimization/sqp.m @ 8047:d54f113aa983
Increase test script tolerances.
| author | Thomas Treichl <Thomas.Treichl@gmx.net> |
|---|---|
| date | Thu, 21 Aug 2008 14:04:04 -0400 |
| parents | df9519e9990c |
| children | 17352ccd860e |
| rev | line source |
|---|---|
| 7017 | 1 ## Copyright (C) 2005, 2006, 2007 John W. Eaton |
| 5289 | 2 ## |
| 3 ## This file is part of Octave. | |
| 4 ## | |
| 5 ## Octave is free software; you can redistribute it and/or modify it | |
| 6 ## under the terms of the GNU General Public License as published by | |
| 7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
| 8 ## your option) any later version. | |
| 5289 | 9 ## |
| 10 ## Octave is distributed in the hope that it will be useful, but | |
| 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 13 ## General Public License for more details. | |
| 14 ## | |
| 15 ## You should have received a copy of the GNU General Public License | |
| 7016 | 16 ## along with Octave; see the file COPYING. If not, see |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 5289 | 18 |
| 19 ## -*- texinfo -*- | |
| 20 ## @deftypefn {Function File} {[@var{x}, @var{obj}, @var{info}, @var{iter}, @var{nf}, @var{lambda}] =} sqp (@var{x}, @var{phi}, @var{g}, @var{h}) | |
| 21 ## Solve the nonlinear program | |
| 6741 | 22 ## @iftex |
| 23 ## @tex | |
| 24 ## $$ | |
| 25 ## \min_x \phi (x) | |
| 26 ## $$ | |
| 27 ## @end tex | |
| 28 ## @end iftex | |
| 29 ## @ifnottex | |
| 5289 | 30 ## |
| 31 ## @example | |
| 32 ## min phi (x) | |
| 33 ## x | |
| 34 ## @end example | |
| 35 ## | |
| 6741 | 36 ## @end ifnottex |
| 37 ## subject to | |
| 5289 | 38 ## @iftex |
| 39 ## @tex | |
| 6741 | 40 ## $$ |
| 41 ## g(x) = 0 \qquad h(x) \geq 0 | |
| 42 ## $$ | |
| 5289 | 43 ## @end tex |
| 44 ## @end iftex | |
| 6741 | 45 ## @ifnottex |
| 5289 | 46 ## |
| 47 ## @example | |
| 48 ## g(x) = 0 | |
| 49 ## h(x) >= 0 | |
| 50 ## @end example | |
| 6741 | 51 ## @end ifnottex |
| 5289 | 52 ## |
| 53 ## @noindent | |
| 54 ## using a successive quadratic programming method. | |
| 55 ## | |
| 56 ## The first argument is the initial guess for the vector @var{x}. | |
| 57 ## | |
| 7001 | 58 ## The second argument is a function handle pointing to the objective |
| 5289 | 59 ## function. The objective function must be of the form |
| 60 ## | |
| 61 ## @example | |
| 62 ## y = phi (x) | |
| 63 ## @end example | |
| 64 ## | |
| 65 ## @noindent | |
| 66 ## in which @var{x} is a vector and @var{y} is a scalar. | |
| 67 ## | |
| 68 ## The second argument may also be a 2- or 3-element cell array of | |
| 69 ## function handles. The first element should point to the objective | |
| 70 ## function, the second should point to a function that computes the | |
| 71 ## gradient of the objective function, and the third should point to a | |
| 72 ## function to compute the hessian of the objective function. If the | |
| 73 ## gradient function is not supplied, the gradient is computed by finite | |
| 74 ## differences. If the hessian function is not supplied, a BFGS update | |
| 75 ## formula is used to approximate the hessian. | |
| 76 ## | |
| 77 ## If supplied, the gradient function must be of the form | |
| 78 ## | |
| 79 ## @example | |
| 7031 | 80 ## g = gradient (x) |
| 5289 | 81 ## @end example |
| 82 ## | |
| 83 ## @noindent | |
| 84 ## in which @var{x} is a vector and @var{g} is a vector. | |
| 85 ## | |
| 86 ## If supplied, the hessian function must be of the form | |
| 87 ## | |
| 88 ## @example | |
| 7031 | 89 ## h = hessian (x) |
| 5289 | 90 ## @end example |
| 91 ## | |
| 92 ## @noindent | |
| 93 ## in which @var{x} is a vector and @var{h} is a matrix. | |
| 94 ## | |
| 95 ## The third and fourth arguments are function handles pointing to | |
| 96 ## functions that compute the equality constraints and the inequality | |
| 97 ## constraints, respectively. | |
| 98 ## | |
| 99 ## If your problem does not have equality (or inequality) constraints, | |
| 100 ## you may pass an empty matrix for @var{cef} (or @var{cif}). | |
| 101 ## | |
| 102 ## If supplied, the equality and inequality constraint functions must be | |
| 103 ## of the form | |
| 104 ## | |
| 105 ## @example | |
| 7031 | 106 ## r = f (x) |
| 5289 | 107 ## @end example |
| 108 ## | |
| 109 ## @noindent | |
| 110 ## in which @var{x} is a vector and @var{r} is a vector. | |
| 111 ## | |
| 112 ## The third and fourth arguments may also be 2-element cell arrays of | |
| 113 ## function handles. The first element should point to the constraint | |
| 114 ## function and the second should point to a function that computes the | |
| 115 ## gradient of the constraint function: | |
| 116 ## | |
| 6741 | 117 ## @iftex |
| 118 ## @tex | |
| 119 ## $$ | |
| 120 ## \Bigg( {\partial f(x) \over \partial x_1}, | |
| 121 ## {\partial f(x) \over \partial x_2}, \ldots, | |
| 122 ## {\partial f(x) \over \partial x_N} \Bigg)^T | |
| 123 ## $$ | |
| 124 ## @end tex | |
| 125 ## @end iftex | |
| 126 ## @ifnottex | |
| 5289 | 127 ## @example |
| 128 ## [ d f(x) d f(x) d f(x) ] | |
| 129 ## transpose ( [ ------ ----- ... ------ ] ) | |
| 130 ## [ dx_1 dx_2 dx_N ] | |
| 131 ## @end example | |
| 6741 | 132 ## @end ifnottex |
| 5289 | 133 ## |
| 134 ## Here is an example of calling @code{sqp}: | |
| 135 ## | |
| 136 ## @example | |
| 7031 | 137 ## function r = g (x) |
| 138 ## r = [ sumsq(x)-10; | |
| 139 ## x(2)*x(3)-5*x(4)*x(5); | |
| 140 ## x(1)^3+x(2)^3+1 ]; | |
| 141 ## endfunction | |
| 142 ## | |
| 143 ## function obj = phi (x) | |
| 144 ## obj = exp(prod(x)) - 0.5*(x(1)^3+x(2)^3+1)^2; | |
| 145 ## endfunction | |
| 5289 | 146 ## |
| 7031 | 147 ## x0 = [-1.8; 1.7; 1.9; -0.8; -0.8]; |
| 148 ## | |
| 149 ## [x, obj, info, iter, nf, lambda] = sqp (x0, @@phi, @@g, []) | |
| 5289 | 150 ## |
| 7031 | 151 ## x = |
| 152 ## | |
| 153 ## -1.71714 | |
| 154 ## 1.59571 | |
| 155 ## 1.82725 | |
| 156 ## -0.76364 | |
| 157 ## -0.76364 | |
| 5289 | 158 ## |
| 7031 | 159 ## obj = 0.053950 |
| 160 ## info = 101 | |
| 161 ## iter = 8 | |
| 162 ## nf = 10 | |
| 163 ## lambda = | |
| 164 ## | |
| 165 ## -0.0401627 | |
| 166 ## 0.0379578 | |
| 167 ## -0.0052227 | |
| 5289 | 168 ## @end example |
| 169 ## | |
| 170 ## The value returned in @var{info} may be one of the following: | |
| 171 ## @table @asis | |
| 172 ## @item 101 | |
| 173 ## The algorithm terminated because the norm of the last step was less | |
| 174 ## than @code{tol * norm (x))} (the value of tol is currently fixed at | |
| 175 ## @code{sqrt (eps)}---edit @file{sqp.m} to modify this value. | |
| 176 ## @item 102 | |
| 177 ## The BFGS update failed. | |
| 178 ## @item 103 | |
| 179 ## The maximum number of iterations was reached (the maximum number of | |
| 180 ## allowed iterations is currently fixed at 100---edit @file{sqp.m} to | |
| 181 ## increase this value). | |
| 182 ## @end table | |
| 5642 | 183 ## @seealso{qp} |
| 5289 | 184 ## @end deftypefn |
| 185 | |
| 6768 | 186 function [x, obj, info, iter, nf, lambda] = sqp (x, objf, cef, cif, lb, ub, maxiter, tolerance) |
| 5289 | 187 |
| 6768 | 188 global __sqp_nfun__; |
| 5289 | 189 global __sqp_obj_fun__; |
| 190 global __sqp_ce_fun__; | |
| 191 global __sqp_ci_fun__; | |
| 6768 | 192 global __sqp_cif__; |
| 193 global __sqp_cifcn__; | |
| 5289 | 194 |
| 6768 | 195 if (nargin >= 2 && nargin <= 8 && nargin != 5) |
| 5289 | 196 |
| 197 ## Choose an initial NxN symmetric positive definite Hessan | |
| 198 ## approximation B. | |
| 199 | |
| 200 n = length (x); | |
| 201 | |
| 202 ## Evaluate objective function, constraints, and gradients at initial | |
| 203 ## value of x. | |
| 204 ## | |
| 205 ## obj_fun | |
| 206 ## obj_grad | |
| 207 ## ce_fun -- equality constraint functions | |
| 208 ## ci_fun -- inequality constraint functions | |
| 209 ## A == [grad_{x_1} cx_fun, grad_{x_2} cx_fun, ..., grad_{x_n} cx_fun]^T | |
| 210 | |
| 211 obj_grd = @fd_obj_grd; | |
| 212 have_hess = 0; | |
| 213 if (iscell (objf)) | |
| 214 if (length (objf) > 0) | |
| 215 __sqp_obj_fun__ = obj_fun = objf{1}; | |
| 216 if (length (objf) > 1) | |
| 217 obj_grd = objf{2}; | |
| 218 if (length (objf) > 2) | |
| 219 obj_hess = objf{3}; | |
| 220 have_hess = 1; | |
| 221 endif | |
| 222 endif | |
| 223 else | |
| 224 error ("sqp: invalid objective function"); | |
| 225 endif | |
| 226 else | |
| 227 __sqp_obj_fun__ = obj_fun = objf; | |
| 228 endif | |
| 229 | |
| 230 ce_fun = @empty_cf; | |
| 231 ce_grd = @empty_jac; | |
| 232 if (nargin > 2) | |
| 233 ce_grd = @fd_ce_jac; | |
| 234 if (iscell (cef)) | |
| 235 if (length (cef) > 0) | |
| 236 __sqp_ce_fun__ = ce_fun = cef{1}; | |
| 237 if (length (cef) > 1) | |
| 238 ce_grd = cef{2}; | |
| 239 endif | |
| 240 else | |
| 241 error ("sqp: invalid equality constraint function"); | |
| 242 endif | |
| 243 elseif (! isempty (cef)) | |
| 244 ce_fun = cef; | |
| 245 endif | |
| 246 endif | |
| 247 __sqp_ce_fun__ = ce_fun; | |
| 248 | |
| 249 ci_fun = @empty_cf; | |
| 250 ci_grd = @empty_jac; | |
| 6768 | 251 |
| 5289 | 252 if (nargin > 3) |
| 6768 | 253 ## constraint function given by user with possibly gradient |
| 254 __sqp_cif__ = cif; | |
| 255 ## constraint function given by user without gradient | |
| 256 __sqp_cifcn__ = @empty_cf; | |
| 257 if (iscell (__sqp_cif__)) | |
| 258 if (length (__sqp_cif__) > 0) | |
| 259 __sqp_cifcn__ = __sqp_cif__{1}; | |
| 260 endif | |
| 261 elseif (! isempty (__sqp_cif__)) | |
| 262 __sqp_cifcn__ = __sqp_cif__; | |
| 263 endif | |
| 264 | |
| 265 if (nargin < 5) | |
| 266 ci_grd = @fd_ci_jac; | |
| 267 if (iscell (cif)) | |
| 268 if (length (cif) > 0) | |
| 269 __sqp_ci_fun__ = ci_fun = cif{1}; | |
| 270 if (length (cif) > 1) | |
| 271 ci_grd = cif{2}; | |
| 272 endif | |
| 273 else | |
| 274 error ("sqp: invalid equality constraint function"); | |
| 5289 | 275 endif |
| 6768 | 276 elseif (! isempty (cif)) |
| 277 ci_fun = cif; | |
| 278 endif | |
| 279 else | |
| 280 global __sqp_lb__; | |
| 281 if (isvector (lb)) | |
| 282 __sqp_lb__ = lb; | |
| 283 elseif (isempty (lb)) | |
|
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284 if (isa (x, "single")) |
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285 __sqp_lb__ = -realmax ("single"); |
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286 else |
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287 __sqp_lb__ = -realmax; |
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288 endif |
| 5289 | 289 else |
| 6768 | 290 error ("sqp: invalid lower bound"); |
| 5289 | 291 endif |
| 6768 | 292 |
| 293 global __sqp_ub__; | |
| 294 if (isvector (ub)) | |
| 295 __sqp_ub__ = ub; | |
| 296 elseif (isempty (lb)) | |
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297 if (isa (x, "single")) |
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298 __sqp_ub__ = realmax ("single"); |
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299 else |
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300 __sqp_ub__ = realmax; |
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parents:
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301 endif |
| 6768 | 302 else |
| 303 error ("sqp: invalid upper bound"); | |
| 304 endif | |
| 305 | |
| 306 if (lb > ub) | |
| 307 error ("sqp: upper bound smaller than lower bound"); | |
| 308 endif | |
| 309 __sqp_ci_fun__ = ci_fun = @cf_ub_lb; | |
| 310 ci_grd = @cigrad_ub_lb; | |
| 311 endif | |
| 312 __sqp_ci_fun__ = ci_fun; | |
| 313 endif | |
| 314 | |
| 315 iter_max = 100; | |
| 316 if (nargin > 6 && ! isempty (maxiter)) | |
| 6921 | 317 if (isscalar (maxiter) && maxiter > 0 && round (maxiter) == maxiter) |
| 6768 | 318 iter_max = maxiter; |
| 319 else | |
| 320 error ("sqp: invalid number of maximum iterations"); | |
| 5289 | 321 endif |
| 322 endif | |
| 323 | |
| 6768 | 324 tol = sqrt (eps); |
| 325 if (nargin > 7 && ! isempty (tolerance)) | |
| 326 if (isscalar (tolerance) && tolerance > 0) | |
| 327 tol = tolerance; | |
| 328 else | |
| 329 error ("sqp: invalid value for tolerance"); | |
| 330 endif | |
| 331 endif | |
| 5289 | 332 |
| 333 iter = 0; | |
| 334 | |
| 335 obj = feval (obj_fun, x); | |
| 6768 | 336 __sqp_nfun__ = 1; |
| 5289 | 337 |
| 338 c = feval (obj_grd, x); | |
| 339 | |
| 6382 | 340 if (have_hess) |
| 341 B = feval (obj_hess, x); | |
| 342 else | |
| 343 B = eye (n, n); | |
| 344 endif | |
| 345 | |
| 5289 | 346 ce = feval (ce_fun, x); |
| 347 F = feval (ce_grd, x); | |
| 348 | |
| 349 ci = feval (ci_fun, x); | |
| 350 C = feval (ci_grd, x); | |
| 351 | |
| 352 A = [F; C]; | |
| 353 | |
| 354 ## Choose an initial lambda (x is provided by the caller). | |
| 355 | |
| 356 lambda = 100 * ones (rows (A), 1); | |
| 357 | |
| 358 qp_iter = 1; | |
| 359 alpha = 1; | |
| 360 | |
| 361 ## report (); | |
| 362 | |
| 6768 | 363 ## report (iter, qp_iter, alpha, __sqp_nfun__, obj); |
| 5289 | 364 |
| 6527 | 365 info = 0; |
| 366 | |
| 5289 | 367 while (++iter < iter_max) |
| 368 | |
| 369 ## Check convergence. This is just a simple check on the first | |
| 370 ## order necessary conditions. | |
| 371 | |
| 372 ## IDX is the indices of the active inequality constraints. | |
| 373 | |
| 374 nr_f = rows (F); | |
| 375 | |
| 376 lambda_e = lambda((1:nr_f)'); | |
| 377 lambda_i = lambda((nr_f+1:end)'); | |
| 378 | |
| 379 con = [ce; ci]; | |
| 380 | |
| 381 t0 = norm (c - A' * lambda); | |
| 382 t1 = norm (ce); | |
| 383 t2 = all (ci >= 0); | |
| 384 t3 = all (lambda_i >= 0); | |
| 385 t4 = norm (lambda .* con); | |
| 386 | |
| 387 if (t2 && t3 && max ([t0; t1; t4]) < tol) | |
| 388 break; | |
| 389 endif | |
| 390 | |
| 391 ## Compute search direction p by solving QP. | |
| 392 | |
| 393 g = -ce; | |
| 394 d = -ci; | |
| 395 | |
| 396 ## Discard inequality constraints that have -Inf bounds since those | |
| 397 ## will never be active. | |
| 398 idx = isinf (d) & d < 0; | |
| 399 d(idx) = []; | |
| 400 C(idx,:) = []; | |
| 401 | |
| 402 [p, obj_qp, INFO, lambda] = qp (x, B, c, F, g, [], [], d, C, | |
| 403 Inf * ones (size (d))); | |
| 404 | |
| 405 info = INFO.info; | |
| 406 | |
| 407 ## Check QP solution and attempt to recover if it has failed. | |
| 408 | |
| 409 ## Choose mu such that p is a descent direction for the chosen | |
| 410 ## merit function phi. | |
| 411 | |
| 412 [x_new, alpha, obj_new] = linesearch_L1 (x, p, obj_fun, obj_grd, | |
| 413 ce_fun, ci_fun, lambda, obj); | |
| 414 | |
| 415 ## Evaluate objective function, constraints, and gradients at | |
| 416 ## x_new. | |
| 417 | |
| 418 c_new = feval (obj_grd, x_new); | |
| 419 | |
| 420 ce_new = feval (ce_fun, x_new); | |
| 421 F_new = feval (ce_grd, x_new); | |
| 422 | |
| 423 ci_new = feval (ci_fun, x_new); | |
| 424 C_new = feval (ci_grd, x_new); | |
| 425 | |
| 426 A_new = [F_new; C_new]; | |
| 427 | |
| 428 ## Set | |
| 429 ## | |
| 430 ## s = alpha * p | |
| 431 ## y = grad_x L (x_new, lambda) - grad_x L (x, lambda}) | |
| 432 | |
| 433 y = c_new - c; | |
| 434 | |
| 435 if (! isempty (A)) | |
| 436 t = ((A_new - A)'*lambda); | |
| 437 y -= t; | |
| 438 endif | |
| 439 | |
| 440 delx = x_new - x; | |
| 441 | |
| 442 if (norm (delx) < tol * norm (x)) | |
| 443 info = 101; | |
| 444 break; | |
| 445 endif | |
| 446 | |
| 447 if (have_hess) | |
| 448 | |
| 449 B = feval (obj_hess, x); | |
| 450 | |
| 451 else | |
| 452 | |
| 453 ## Update B using a quasi-Newton formula. | |
| 454 | |
| 455 delxt = delx'; | |
| 456 | |
| 457 ## Damped BFGS. Or maybe we would actually want to use the Hessian | |
| 458 ## of the Lagrangian, computed directly. | |
| 459 | |
| 460 d1 = delxt*B*delx; | |
| 461 | |
| 462 t1 = 0.2 * d1; | |
| 463 t2 = delxt*y; | |
| 464 | |
| 465 if (t2 < t1) | |
| 466 theta = 0.8*d1/(d1 - t2); | |
| 467 else | |
| 468 theta = 1; | |
| 469 endif | |
| 470 | |
| 471 r = theta*y + (1-theta)*B*delx; | |
| 472 | |
| 473 d2 = delxt*r; | |
| 474 | |
| 475 if (d1 == 0 || d2 == 0) | |
| 476 info = 102; | |
| 477 break; | |
| 478 endif | |
| 479 | |
| 480 B = B - B*delx*delxt*B/d1 + r*r'/d2; | |
| 481 | |
| 482 endif | |
| 483 | |
| 484 x = x_new; | |
| 485 | |
| 486 obj = obj_new; | |
| 487 | |
| 488 c = c_new; | |
| 489 | |
| 490 ce = ce_new; | |
| 491 F = F_new; | |
| 492 | |
| 493 ci = ci_new; | |
| 494 C = C_new; | |
| 495 | |
| 496 A = A_new; | |
| 497 | |
| 6768 | 498 ## report (iter, qp_iter, alpha, __sqp_nfun__, obj); |
| 5289 | 499 |
| 500 endwhile | |
| 501 | |
| 502 if (iter >= iter_max) | |
| 503 info = 103; | |
| 504 endif | |
| 505 | |
| 6768 | 506 nf = __sqp_nfun__; |
| 5289 | 507 |
| 508 else | |
| 509 | |
| 6046 | 510 print_usage (); |
| 5289 | 511 |
| 512 endif | |
| 513 | |
| 7399 | 514 endfunction |
| 5289 | 515 |
| 516 | |
| 517 function [merit, obj] = phi_L1 (obj, obj_fun, ce_fun, ci_fun, x, mu) | |
| 518 | |
| 6768 | 519 global __sqp_nfun__; |
| 5289 | 520 |
| 521 ce = feval (ce_fun, x); | |
| 522 ci = feval (ci_fun, x); | |
| 523 | |
| 524 idx = ci < 0; | |
| 525 | |
| 526 con = [ce; ci(idx)]; | |
| 527 | |
| 528 if (isempty (obj)) | |
| 529 obj = feval (obj_fun, x); | |
| 6768 | 530 __sqp_nfun__++; |
| 5289 | 531 endif |
| 532 | |
| 533 merit = obj; | |
| 534 t = norm (con, 1) / mu; | |
| 535 | |
| 536 if (! isempty (t)) | |
| 537 merit += t; | |
| 538 endif | |
| 539 | |
| 7399 | 540 endfunction |
| 5289 | 541 |
| 542 | |
| 543 function [x_new, alpha, obj] = linesearch_L1 (x, p, obj_fun, obj_grd, | |
| 544 ce_fun, ci_fun, lambda, obj) | |
| 545 | |
| 546 ## Choose parameters | |
| 547 ## | |
| 548 ## eta in the range (0, 0.5) | |
| 549 ## tau in the range (0, 1) | |
| 550 | |
| 551 eta = 0.25; | |
| 552 tau = 0.5; | |
| 553 | |
| 554 delta_bar = sqrt (eps); | |
| 555 | |
| 556 if (isempty (lambda)) | |
| 557 mu = 1 / delta_bar; | |
| 558 else | |
| 559 mu = 1 / (norm (lambda, Inf) + delta_bar); | |
| 560 endif | |
| 561 | |
| 562 alpha = 1; | |
| 563 | |
| 564 c = feval (obj_grd, x); | |
| 565 ce = feval (ce_fun, x); | |
| 566 | |
| 567 [phi_x_mu, obj] = phi_L1 (obj, obj_fun, ce_fun, ci_fun, x, mu); | |
| 568 | |
| 569 D_phi_x_mu = c' * p; | |
| 570 d = feval (ci_fun, x); | |
| 571 ## only those elements of d corresponding | |
| 572 ## to violated constraints should be included. | |
| 573 idx = d < 0; | |
| 574 t = - norm ([ce; d(idx)], 1) / mu; | |
| 575 if (! isempty (t)) | |
| 576 D_phi_x_mu += t; | |
| 577 endif | |
| 578 | |
| 579 while (1) | |
| 580 [p1, obj] = phi_L1 ([], obj_fun, ce_fun, ci_fun, x+alpha*p, mu); | |
| 581 p2 = phi_x_mu+eta*alpha*D_phi_x_mu; | |
| 582 if (p1 > p2) | |
| 583 ## Reset alpha = tau_alpha * alpha for some tau_alpha in the | |
| 584 ## range (0, tau). | |
| 585 tau_alpha = 0.9 * tau; ## ?? | |
| 586 alpha = tau_alpha * alpha; | |
| 587 else | |
| 588 break; | |
| 589 endif | |
| 590 endwhile | |
| 591 | |
| 592 ## Set x_new = x + alpha * p; | |
| 593 | |
| 594 x_new = x + alpha * p; | |
| 595 | |
| 7399 | 596 endfunction |
| 5289 | 597 |
| 598 | |
| 599 function report (iter, qp_iter, alpha, nfun, obj) | |
| 600 | |
| 601 if (nargin == 0) | |
| 602 printf (" Itn ItQP Step Nfun Objective\n"); | |
| 603 else | |
| 604 printf ("%5d %4d %8.1g %5d %13.6e\n", iter, qp_iter, alpha, nfun, obj); | |
| 605 endif | |
| 606 | |
| 7399 | 607 endfunction |
| 5289 | 608 |
| 609 | |
| 610 function grd = fdgrd (f, x) | |
| 611 | |
| 612 if (! isempty (f)) | |
| 613 y0 = feval (f, x); | |
| 614 nx = length (x); | |
| 615 grd = zeros (nx, 1); | |
| 616 deltax = sqrt (eps); | |
| 617 for i = 1:nx | |
| 618 t = x(i); | |
| 619 x(i) += deltax; | |
| 620 grd(i) = (feval (f, x) - y0) / deltax; | |
| 621 x(i) = t; | |
| 622 endfor | |
| 623 else | |
| 624 grd = zeros (0, 1); | |
| 625 endif | |
| 626 | |
| 7399 | 627 endfunction |
| 5289 | 628 |
| 629 | |
| 630 function jac = fdjac (f, x) | |
| 6768 | 631 nx = length (x); |
| 5289 | 632 if (! isempty (f)) |
| 633 y0 = feval (f, x); | |
| 634 nf = length (y0); | |
| 635 nx = length (x); | |
| 636 jac = zeros (nf, nx); | |
| 637 deltax = sqrt (eps); | |
| 638 for i = 1:nx | |
| 639 t = x(i); | |
| 640 x(i) += deltax; | |
| 641 jac(:,i) = (feval (f, x) - y0) / deltax; | |
| 642 x(i) = t; | |
| 643 endfor | |
| 644 else | |
| 645 jac = zeros (0, nx); | |
| 646 endif | |
| 647 | |
| 7399 | 648 endfunction |
| 5289 | 649 |
| 650 | |
| 651 function grd = fd_obj_grd (x) | |
| 652 | |
| 653 global __sqp_obj_fun__; | |
| 654 | |
| 655 grd = fdgrd (__sqp_obj_fun__, x); | |
| 656 | |
| 7399 | 657 endfunction |
| 5289 | 658 |
| 659 | |
| 660 function res = empty_cf (x) | |
| 661 | |
| 662 res = zeros (0, 1); | |
| 663 | |
| 7399 | 664 endfunction |
| 5289 | 665 |
| 666 | |
| 667 function res = empty_jac (x) | |
| 668 | |
| 669 res = zeros (0, length (x)); | |
| 670 | |
| 7399 | 671 endfunction |
| 5289 | 672 |
| 673 | |
| 674 function jac = fd_ce_jac (x) | |
| 675 | |
| 676 global __sqp_ce_fun__; | |
| 677 | |
| 678 jac = fdjac (__sqp_ce_fun__, x); | |
| 679 | |
| 7399 | 680 endfunction |
| 5289 | 681 |
| 682 | |
| 683 function jac = fd_ci_jac (x) | |
| 684 | |
| 6768 | 685 global __sqp_cifcn__; |
| 686 ## __sqp_cifcn__ = constraint function without gradients and lb or ub | |
| 687 jac = fdjac (__sqp_cifcn__, x); | |
| 688 | |
| 7399 | 689 endfunction |
| 6768 | 690 |
| 7017 | 691 |
| 6768 | 692 function res = cf_ub_lb (x) |
| 5289 | 693 |
| 6768 | 694 ## combine constraint function with ub and lb |
| 695 global __sqp_cifcn__ __sqp_lb__ __sqp_ub__ | |
| 696 | |
| 697 res = [x-__sqp_lb__; __sqp_ub__-x]; | |
| 698 | |
| 699 if (! isempty (__sqp_cifcn__)) | |
| 700 res = [feval(__sqp_cifcn__,x); x-__sqp_lb__; __sqp_ub__-x]; | |
| 701 endif | |
| 5289 | 702 |
| 7399 | 703 endfunction |
| 6768 | 704 |
| 7017 | 705 |
| 6768 | 706 function res = cigrad_ub_lb (x) |
| 707 | |
| 708 global __sqp_cif__ | |
| 709 | |
| 710 res = [eye(numel(x)); -eye(numel(x))]; | |
| 711 | |
| 712 cigradfcn = @fd_ci_jac; | |
| 713 | |
| 714 if (iscell (__sqp_cif__) && length (__sqp_cif__) > 1) | |
| 715 cigradfcn = __sqp_cif__{2}; | |
| 716 endif | |
| 717 | |
| 718 if (! isempty (cigradfcn)) | |
| 719 res = [feval(cigradfcn,x); eye(numel(x)); -eye(numel(x))]; | |
| 720 endif | |
| 721 | |
| 7399 | 722 endfunction |
| 7361 | 723 |
| 7371 | 724 %!function r = g (x) |
| 725 %! r = [sumsq(x)-10; | |
| 726 %! x(2)*x(3)-5*x(4)*x(5); | |
| 727 %! x(1)^3+x(2)^3+1 ]; | |
| 7361 | 728 %! |
| 7371 | 729 %!function obj = phi (x) |
| 730 %! obj = exp(prod(x)) - 0.5*(x(1)^3+x(2)^3+1)^2; | |
| 7361 | 731 %! |
| 732 %!test | |
| 733 %! x0 = [-1.8; 1.7; 1.9; -0.8; -0.8]; | |
| 734 %! | |
| 7381 | 735 %! [x, obj, info, iter, nf, lambda] = sqp (x0, @phi, @g, []); |
| 7361 | 736 %! |
| 737 %! x_opt = [-1.717143501952599; | |
| 738 %! 1.595709610928535; | |
| 739 %! 1.827245880097156; | |
| 740 %! -0.763643103133572; | |
| 741 %! -0.763643068453300]; | |
| 742 %! | |
| 7371 | 743 %! obj_opt = 0.0539498477702739; |
| 7361 | 744 %! |
|
8047
d54f113aa983
Increase test script tolerances.
Thomas Treichl <Thomas.Treichl@gmx.net>
parents:
7795
diff
changeset
|
745 %! assert (all (abs (x-x_opt) < 5*sqrt (eps)) && abs (obj-obj_opt) < sqrt (eps)); |