Mercurial > octave
annotate scripts/optimization/sqp.m @ 13207:88bd1d1d6657 stable
Reword sqp's docstring
| author | Jordi Gutiérrez Hermoso <jordigh@octave.org> |
|---|---|
| date | Sat, 24 Sep 2011 11:04:24 -0500 |
| parents | c792872f8942 |
| children | 571557ddabb9 |
| rev | line source |
|---|---|
| 11523 | 1 ## Copyright (C) 2005-2011 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 -*- | |
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20 ## @deftypefn {Function File} {[@var{x}, @var{obj}, @var{info}, @var{iter}, @var{nf}, @var{lambda}] =} sqp (@var{x0}, @var{phi}) |
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21 ## @deftypefnx {Function File} {[@dots{}] =} sqp (@var{x0}, @var{phi}, @var{g}) |
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22 ## @deftypefnx {Function File} {[@dots{}] =} sqp (@var{x0}, @var{phi}, @var{g}, @var{h}) |
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23 ## @deftypefnx {Function File} {[@dots{}] =} sqp (@var{x0}, @var{phi}, @var{g}, @var{h}, @var{lb}, @var{ub}) |
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24 ## @deftypefnx {Function File} {[@dots{}] =} sqp (@var{x0}, @var{phi}, @var{g}, @var{h}, @var{lb}, @var{ub}, @var{maxiter}) |
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25 ## @deftypefnx {Function File} {[@dots{}] =} sqp (@var{x0}, @var{phi}, @var{g}, @var{h}, @var{lb}, @var{ub}, @var{maxiter}, @var{tol}) |
| 5289 | 26 ## Solve the nonlinear program |
| 6741 | 27 ## @tex |
| 28 ## $$ | |
| 29 ## \min_x \phi (x) | |
| 30 ## $$ | |
| 31 ## @end tex | |
| 32 ## @ifnottex | |
| 5289 | 33 ## |
| 34 ## @example | |
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35 ## @group |
| 5289 | 36 ## min phi (x) |
| 37 ## x | |
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38 ## @end group |
| 5289 | 39 ## @end example |
| 40 ## | |
| 6741 | 41 ## @end ifnottex |
| 42 ## subject to | |
| 5289 | 43 ## @tex |
| 6741 | 44 ## $$ |
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45 ## g(x) = 0 \qquad h(x) \geq 0 \qquad lb \leq x \leq ub |
| 6741 | 46 ## $$ |
| 5289 | 47 ## @end tex |
| 6741 | 48 ## @ifnottex |
| 5289 | 49 ## |
| 50 ## @example | |
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51 ## @group |
| 5289 | 52 ## g(x) = 0 |
| 53 ## h(x) >= 0 | |
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54 ## lb <= x <= ub |
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55 ## @end group |
| 5289 | 56 ## @end example |
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57 ## |
| 6741 | 58 ## @end ifnottex |
| 5289 | 59 ## @noindent |
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60 ## using a sequential quadratic programming method. |
| 5289 | 61 ## |
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62 ## The first argument is the initial guess for the vector @var{x0}. |
| 5289 | 63 ## |
| 7001 | 64 ## The second argument is a function handle pointing to the objective |
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65 ## function @var{phi}. The objective function must accept one vector |
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66 ## argument and return a scalar. |
| 5289 | 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 | |
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72 ## function that computes the Hessian of the objective function. If the |
| 5289 | 73 ## gradient function is not supplied, the gradient is computed by finite |
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74 ## differences. If the Hessian function is not supplied, a BFGS update |
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75 ## formula is used to approximate the Hessian. |
| 5289 | 76 ## |
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77 ## When supplied, the gradient function @code{@var{phi}@{2@}} must accept |
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78 ## one vector argument and return a vector. When supplifed, the Hessian |
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79 ## function @code{@var{phi}@{3@}} must accept one vector argument and |
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80 ## return a matrix. |
| 5289 | 81 ## |
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82 ## The third and fourth arguments @var{g} and @var{h} are function |
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83 ## handles pointing to functions that compute the equality constraints |
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84 ## and the inequality constraints, respectively. If the problem does |
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85 ## not have equality (or inequality) constraints, then use an empty |
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86 ## matrix ([]) for @var{g} (or @var{h}). When supplied, these equality |
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87 ## and inequality constraint functions must accept one vector argument |
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88 ## and return a vector. |
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89 ## |
| 5289 | 90 ## The third and fourth arguments may also be 2-element cell arrays of |
| 91 ## function handles. The first element should point to the constraint | |
| 92 ## function and the second should point to a function that computes the | |
| 93 ## gradient of the constraint function: | |
| 6741 | 94 ## @tex |
| 95 ## $$ | |
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96 ## \Bigg( {\partial f(x) \over \partial x_1}, |
| 6741 | 97 ## {\partial f(x) \over \partial x_2}, \ldots, |
| 98 ## {\partial f(x) \over \partial x_N} \Bigg)^T | |
| 99 ## $$ | |
| 100 ## @end tex | |
| 101 ## @ifnottex | |
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102 ## |
| 5289 | 103 ## @example |
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104 ## @group |
| 5289 | 105 ## [ d f(x) d f(x) d f(x) ] |
| 106 ## transpose ( [ ------ ----- ... ------ ] ) | |
| 107 ## [ dx_1 dx_2 dx_N ] | |
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108 ## @end group |
| 5289 | 109 ## @end example |
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110 ## |
| 6741 | 111 ## @end ifnottex |
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112 ## The fifth and sixth arguments, @var{lb} and @var{ub}, contain lower |
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113 ## and upper bounds on @var{x}. These must be consistent with the |
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114 ## equality and inequality constraints @var{g} and @var{h}. If the |
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115 ## arguments are vectors then @var{x}(i) is bound by @var{lb}(i) and |
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116 ## @var{ub}(i). A bound can also be a scalar in which case all elements |
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117 ## of @var{x} will share the same bound. If only one bound (lb, ub) is |
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118 ## specified then the other will default to (-@var{realmax}, |
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119 ## +@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 |
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125 ## stopping 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 ## Either all constraints meet the requested tolerance, or the stepsize, |
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133 ## @tex |
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134 ## $\Delta x,$ |
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135 ## @end tex |
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136 ## @ifnottex |
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137 ## delta @var{x}, |
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138 ## @end ifnottex |
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139 ## is less than @code{@var{tol} * norm (x)}. |
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140 ## |
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141 ## @item 102 |
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142 ## The BFGS update failed. |
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143 ## |
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144 ## @item 103 |
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145 ## The maximum number of iterations was reached. |
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146 ## @end table |
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147 ## |
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148 ## An example of calling @code{sqp}: |
| 5289 | 149 ## |
| 150 ## @example | |
| 7031 | 151 ## function r = g (x) |
| 152 ## r = [ sumsq(x)-10; | |
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153 ## x(2)*x(3)-5*x(4)*x(5); |
| 7031 | 154 ## x(1)^3+x(2)^3+1 ]; |
| 155 ## endfunction | |
| 156 ## | |
| 157 ## function obj = phi (x) | |
| 158 ## obj = exp(prod(x)) - 0.5*(x(1)^3+x(2)^3+1)^2; | |
| 159 ## endfunction | |
| 5289 | 160 ## |
| 7031 | 161 ## x0 = [-1.8; 1.7; 1.9; -0.8; -0.8]; |
| 162 ## | |
| 163 ## [x, obj, info, iter, nf, lambda] = sqp (x0, @@phi, @@g, []) | |
| 5289 | 164 ## |
| 7031 | 165 ## x = |
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166 ## |
| 7031 | 167 ## -1.71714 |
| 168 ## 1.59571 | |
| 169 ## 1.82725 | |
| 170 ## -0.76364 | |
| 171 ## -0.76364 | |
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172 ## |
| 7031 | 173 ## obj = 0.053950 |
| 174 ## info = 101 | |
| 175 ## iter = 8 | |
| 176 ## nf = 10 | |
| 177 ## lambda = | |
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178 ## |
| 7031 | 179 ## -0.0401627 |
| 180 ## 0.0379578 | |
| 181 ## -0.0052227 | |
| 5289 | 182 ## @end example |
| 183 ## | |
| 5642 | 184 ## @seealso{qp} |
| 5289 | 185 ## @end deftypefn |
| 186 | |
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187 function [x, obj, info, iter, nf, lambda] = sqp (x0, objf, cef, cif, lb, ub, maxiter, tolerance) |
| 5289 | 188 |
| 6768 | 189 global __sqp_nfun__; |
| 5289 | 190 global __sqp_obj_fun__; |
| 191 global __sqp_ce_fun__; | |
| 192 global __sqp_ci_fun__; | |
| 6768 | 193 global __sqp_cif__; |
| 194 global __sqp_cifcn__; | |
| 5289 | 195 |
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196 if (nargin < 2 || nargin > 8 || nargin == 5) |
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197 print_usage (); |
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198 endif |
| 5289 | 199 |
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200 if (!isvector (x0)) |
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201 error ("sqp: X0 must be a vector"); |
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202 endif |
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203 if (rows (x0) == 1) |
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204 x0 = x0'; |
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205 endif |
| 5289 | 206 |
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207 obj_grd = @fd_obj_grd; |
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208 have_hess = 0; |
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209 if (iscell (objf)) |
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210 switch (numel (objf)) |
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211 case 1 |
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212 obj_fun = objf{1}; |
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213 case 2 |
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214 obj_fun = objf{1}; |
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215 obj_grd = objf{2}; |
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216 case 3 |
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217 obj_fun = objf{1}; |
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218 obj_grd = objf{2}; |
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219 obj_hess = objf{3}; |
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220 have_hess = 1; |
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221 otherwise |
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222 error ("sqp: invalid objective function specification"); |
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223 endswitch |
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224 else |
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225 obj_fun = objf; # No cell array, only obj_fun set |
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226 endif |
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227 __sqp_obj_fun__ = obj_fun; |
| 5289 | 228 |
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229 ce_fun = @empty_cf; |
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230 ce_grd = @empty_jac; |
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231 if (nargin > 2) |
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232 ce_grd = @fd_ce_jac; |
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233 if (iscell (cef)) |
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234 switch (numel (cef)) |
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235 case 1 |
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236 ce_fun = cef{1}; |
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237 case 2 |
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238 ce_fun = cef{1}; |
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239 ce_grd = cef{2}; |
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240 otherwise |
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241 error ("sqp: invalid equality constraint function specification"); |
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242 endswitch |
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243 elseif (! isempty (cef)) |
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244 ce_fun = cef; # No cell array, only constraint equality function set |
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245 endif |
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246 endif |
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247 __sqp_ce_fun__ = ce_fun; |
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248 |
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249 ci_fun = @empty_cf; |
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250 ci_grd = @empty_jac; |
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251 if (nargin > 3) |
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252 ## constraint function given by user with possible gradient |
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253 __sqp_cif__ = cif; |
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254 ## constraint function given by user without gradient |
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255 __sqp_cifcn__ = @empty_cf; |
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256 if (iscell (cif)) |
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257 if (length (cif) > 0) |
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258 __sqp_cifcn__ = cif{1}; |
| 5289 | 259 endif |
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260 elseif (! isempty (cif)) |
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261 __sqp_cifcn__ = cif; |
| 5289 | 262 endif |
| 263 | |
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264 if (nargin < 5 || (nargin > 5 && isempty (lb) && isempty (ub))) |
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265 ## constraint inequality function only without any bounds |
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266 ci_grd = @fd_ci_jac; |
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267 if (iscell (cif)) |
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268 switch length (cif) |
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269 case {1} |
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270 ci_fun = cif{1}; |
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271 case {2} |
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272 ci_fun = cif{1}; |
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273 ci_grd = cif{2}; |
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274 otherwise |
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275 error ("sqp: invalid inequality constraint function specification"); |
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276 endswitch |
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277 elseif (! isempty (cif)) |
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278 ci_fun = cif; # No cell array, only constraint inequality function set |
| 5289 | 279 endif |
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280 else |
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281 ## constraint inequality function with bounds present |
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282 global __sqp_lb__; |
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283 lb_idx = ub_idx = true (size (x0)); |
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284 ub_grad = - (lb_grad = eye (rows (x0))); |
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285 if (isvector (lb)) |
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286 __sqp_lb__ = tmp_lb = lb(:); |
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287 lb_idx(:) = tmp_idx = (lb != -Inf); |
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288 __sqp_lb__ = __sqp_lb__(tmp_idx, 1); |
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289 lb_grad = lb_grad(lb_idx, :); |
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290 elseif (isempty (lb)) |
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291 if (isa (x0, "single")) |
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292 __sqp_lb__ = tmp_lb = -realmax ("single"); |
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293 else |
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294 __sqp_lb__ = tmp_lb = -realmax; |
| 10549 | 295 endif |
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296 else |
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297 error ("sqp: invalid lower bound"); |
| 6768 | 298 endif |
| 299 | |
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300 global __sqp_ub__; |
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301 if (isvector (ub)) |
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302 __sqp_ub__ = tmp_ub = ub(:); |
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303 ub_idx(:) = tmp_idx = (ub != Inf); |
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304 __sqp_ub__ = __sqp_ub__(tmp_idx, 1); |
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305 ub_grad = ub_grad(ub_idx, :); |
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306 elseif (isempty (ub)) |
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307 if (isa (x0, "single")) |
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308 __sqp_ub__ = tmp_ub = realmax ("single"); |
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309 else |
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310 __sqp_ub__ = tmp_ub = realmax; |
| 10549 | 311 endif |
| 6768 | 312 else |
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313 error ("sqp: invalid upper bound"); |
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314 endif |
| 6768 | 315 |
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316 if (any (tmp_lb > tmp_ub)) |
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317 error ("sqp: upper bound smaller than lower bound"); |
| 6768 | 318 endif |
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319 bounds_grad = [lb_grad; ub_grad]; |
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320 ci_fun = @ (x) cf_ub_lb (x, lb_idx, ub_idx); |
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321 ci_grd = @ (x) cigrad_ub_lb (x, bounds_grad); |
| 6768 | 322 endif |
| 5289 | 323 |
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324 __sqp_ci_fun__ = ci_fun; |
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325 endif # if (nargin > 3) |
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326 |
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327 iter_max = 100; |
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328 if (nargin > 6 && ! isempty (maxiter)) |
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329 if (isscalar (maxiter) && maxiter > 0 && fix (maxiter) == maxiter) |
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330 iter_max = maxiter; |
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331 else |
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332 error ("sqp: invalid number of maximum iterations"); |
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333 endif |
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334 endif |
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335 |
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336 tol = sqrt (eps); |
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337 if (nargin > 7 && ! isempty (tolerance)) |
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338 if (isscalar (tolerance) && tolerance > 0) |
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339 tol = tolerance; |
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340 else |
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341 error ("sqp: invalid value for TOLERANCE"); |
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342 endif |
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343 endif |
| 5289 | 344 |
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345 ## Initialize variables for search loop |
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346 ## Seed x with initial guess and evaluate objective function, constraints, |
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347 ## and gradients at initial value x0. |
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348 ## |
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349 ## obj_fun -- objective function |
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350 ## obj_grad -- objective gradient |
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351 ## ce_fun -- equality constraint functions |
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352 ## ci_fun -- inequality constraint functions |
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353 ## A == [grad_{x_1} cx_fun, grad_{x_2} cx_fun, ..., grad_{x_n} cx_fun]^T |
|
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354 x = x0; |
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355 |
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356 obj = feval (obj_fun, x0); |
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357 __sqp_nfun__ = 1; |
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358 |
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359 c = feval (obj_grd, x0); |
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360 |
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361 ## Choose an initial NxN symmetric positive definite Hessian approximation B. |
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362 n = length (x0); |
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363 if (have_hess) |
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364 B = feval (obj_hess, x0); |
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365 else |
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366 B = eye (n, n); |
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367 endif |
| 5289 | 368 |
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369 ce = feval (ce_fun, x0); |
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370 F = feval (ce_grd, x0); |
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371 |
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372 ci = feval (ci_fun, x0); |
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373 C = feval (ci_grd, x0); |
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374 |
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375 A = [F; C]; |
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376 |
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377 ## Choose an initial lambda (x is provided by the caller). |
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378 lambda = 100 * ones (rows (A), 1); |
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379 |
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380 qp_iter = 1; |
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381 alpha = 1; |
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382 |
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383 info = 0; |
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384 iter = 0; |
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385 # report (); # Called with no arguments to initialize reporting |
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386 # report (iter, qp_iter, alpha, __sqp_nfun__, obj); |
| 5289 | 387 |
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388 while (++iter < iter_max) |
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389 |
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390 ## Check convergence. This is just a simple check on the first |
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391 ## order necessary conditions. |
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392 nr_f = rows (F); |
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393 |
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394 lambda_e = lambda((1:nr_f)'); |
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395 lambda_i = lambda((nr_f+1:end)'); |
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396 |
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397 con = [ce; ci]; |
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398 |
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399 t0 = norm (c - A' * lambda); |
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400 t1 = norm (ce); |
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401 t2 = all (ci >= 0); |
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402 t3 = all (lambda_i >= 0); |
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403 t4 = norm (lambda .* con); |
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404 |
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405 if (t2 && t3 && max ([t0; t1; t4]) < tol) |
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406 info = 101; |
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407 break; |
| 6382 | 408 endif |
| 409 | |
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410 ## Compute search direction p by solving QP. |
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411 g = -ce; |
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412 d = -ci; |
| 5289 | 413 |
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414 [p, obj_qp, INFO, lambda] = qp (x, B, c, F, g, [], [], d, C, |
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415 Inf (size (d))); |
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416 |
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417 info = INFO.info; |
| 5289 | 418 |
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419 ## Check QP solution and attempt to recover if it has failed. |
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420 |
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421 ## Choose mu such that p is a descent direction for the chosen |
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422 ## merit function phi. |
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423 [x_new, alpha, obj_new] = linesearch_L1 (x, p, obj_fun, obj_grd, |
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424 ce_fun, ci_fun, lambda, obj); |
| 5289 | 425 |
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426 ## Evaluate objective function, constraints, and gradients at x_new. |
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427 c_new = feval (obj_grd, x_new); |
| 5289 | 428 |
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429 ce_new = feval (ce_fun, x_new); |
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430 F_new = feval (ce_grd, x_new); |
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431 |
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432 ci_new = feval (ci_fun, x_new); |
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433 C_new = feval (ci_grd, x_new); |
| 5289 | 434 |
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435 A_new = [F_new; C_new]; |
| 5289 | 436 |
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437 ## Set |
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438 ## |
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439 ## s = alpha * p |
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440 ## y = grad_x L (x_new, lambda) - grad_x L (x, lambda}) |
| 6527 | 441 |
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442 y = c_new - c; |
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443 |
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444 if (! isempty (A)) |
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445 t = ((A_new - A)'*lambda); |
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446 y -= t; |
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447 endif |
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448 |
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449 delx = x_new - x; |
| 5289 | 450 |
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451 if (norm (delx) < tol * norm (x)) |
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452 info = 101; |
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453 break; |
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454 endif |
| 5289 | 455 |
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456 if (have_hess) |
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457 |
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458 B = feval (obj_hess, x); |
| 5289 | 459 |
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460 else |
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461 ## Update B using a quasi-Newton formula. |
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462 delxt = delx'; |
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463 |
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464 ## Damped BFGS. Or maybe we would actually want to use the Hessian |
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465 ## of the Lagrangian, computed directly? |
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466 d1 = delxt*B*delx; |
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467 |
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468 t1 = 0.2 * d1; |
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469 t2 = delxt*y; |
| 5289 | 470 |
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471 if (t2 < t1) |
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472 theta = 0.8*d1/(d1 - t2); |
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473 else |
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474 theta = 1; |
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475 endif |
| 5289 | 476 |
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477 r = theta*y + (1-theta)*B*delx; |
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478 |
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479 d2 = delxt*r; |
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480 |
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481 if (d1 == 0 || d2 == 0) |
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482 info = 102; |
| 10549 | 483 break; |
| 5289 | 484 endif |
| 485 | |
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486 B = B - B*delx*delxt*B/d1 + r*r'/d2; |
| 5289 | 487 |
| 488 endif | |
| 489 | |
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490 x = x_new; |
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491 |
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492 obj = obj_new; |
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493 |
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494 c = c_new; |
| 5289 | 495 |
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496 ce = ce_new; |
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497 F = F_new; |
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498 |
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499 ci = ci_new; |
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500 C = C_new; |
| 5289 | 501 |
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502 A = A_new; |
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503 |
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504 # report (iter, qp_iter, alpha, __sqp_nfun__, obj); |
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505 |
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506 endwhile |
| 5289 | 507 |
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508 if (iter >= iter_max) |
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509 info = 103; |
| 5289 | 510 endif |
| 511 | |
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512 nf = __sqp_nfun__; |
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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, | |
| 10549 | 544 ce_fun, ci_fun, lambda, obj) |
| 5289 | 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). | |
|
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585 tau_alpha = 0.9 * tau; # ?? |
| 5289 | 586 alpha = tau_alpha * alpha; |
| 587 else | |
| 588 break; | |
| 589 endif | |
| 590 endwhile | |
| 591 | |
| 592 x_new = x + alpha * p; | |
| 593 | |
| 7399 | 594 endfunction |
| 5289 | 595 |
| 596 | |
| 597 function grd = fdgrd (f, x) | |
| 598 | |
| 599 if (! isempty (f)) | |
| 600 y0 = feval (f, x); | |
| 601 nx = length (x); | |
| 602 grd = zeros (nx, 1); | |
| 603 deltax = sqrt (eps); | |
| 604 for i = 1:nx | |
| 605 t = x(i); | |
| 606 x(i) += deltax; | |
| 607 grd(i) = (feval (f, x) - y0) / deltax; | |
| 608 x(i) = t; | |
| 609 endfor | |
| 610 else | |
| 611 grd = zeros (0, 1); | |
| 612 endif | |
| 613 | |
| 7399 | 614 endfunction |
| 5289 | 615 |
| 616 | |
| 617 function jac = fdjac (f, x) | |
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618 |
| 6768 | 619 nx = length (x); |
| 5289 | 620 if (! isempty (f)) |
| 621 y0 = feval (f, x); | |
| 622 nf = length (y0); | |
| 623 nx = length (x); | |
| 624 jac = zeros (nf, nx); | |
| 625 deltax = sqrt (eps); | |
| 626 for i = 1:nx | |
| 627 t = x(i); | |
| 628 x(i) += deltax; | |
| 629 jac(:,i) = (feval (f, x) - y0) / deltax; | |
| 630 x(i) = t; | |
| 631 endfor | |
| 632 else | |
| 633 jac = zeros (0, nx); | |
| 634 endif | |
| 635 | |
| 7399 | 636 endfunction |
| 5289 | 637 |
| 638 | |
| 639 function grd = fd_obj_grd (x) | |
| 640 | |
| 641 global __sqp_obj_fun__; | |
| 642 | |
| 643 grd = fdgrd (__sqp_obj_fun__, x); | |
| 644 | |
| 7399 | 645 endfunction |
| 5289 | 646 |
| 647 | |
| 648 function res = empty_cf (x) | |
| 649 | |
| 650 res = zeros (0, 1); | |
| 651 | |
| 7399 | 652 endfunction |
| 5289 | 653 |
| 654 | |
| 655 function res = empty_jac (x) | |
| 656 | |
| 657 res = zeros (0, length (x)); | |
| 658 | |
| 7399 | 659 endfunction |
| 5289 | 660 |
| 661 | |
| 662 function jac = fd_ce_jac (x) | |
| 663 | |
| 664 global __sqp_ce_fun__; | |
| 665 | |
| 666 jac = fdjac (__sqp_ce_fun__, x); | |
| 667 | |
| 7399 | 668 endfunction |
| 5289 | 669 |
| 670 | |
| 671 function jac = fd_ci_jac (x) | |
| 672 | |
| 6768 | 673 global __sqp_cifcn__; |
| 674 ## __sqp_cifcn__ = constraint function without gradients and lb or ub | |
| 675 jac = fdjac (__sqp_cifcn__, x); | |
| 676 | |
| 7399 | 677 endfunction |
| 6768 | 678 |
| 7017 | 679 |
|
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680 function res = cf_ub_lb (x, lbidx, ubidx) |
| 5289 | 681 |
| 6768 | 682 ## combine constraint function with ub and lb |
| 683 global __sqp_cifcn__ __sqp_lb__ __sqp_ub__ | |
| 684 | |
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685 if (isempty (__sqp_cifcn__)) |
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686 res = [x(lbidx,1)-__sqp_lb__; __sqp_ub__-x(ubidx,1)]; |
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687 else |
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688 res = [feval(__sqp_cifcn__,x); \ |
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689 x(lbidx,1)-__sqp_lb__; __sqp_ub__-x(ubidx,1)]; |
| 6768 | 690 endif |
| 5289 | 691 |
| 7399 | 692 endfunction |
| 6768 | 693 |
| 7017 | 694 |
|
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695 function res = cigrad_ub_lb (x, bgrad) |
| 6768 | 696 |
| 697 global __sqp_cif__ | |
| 698 | |
| 699 cigradfcn = @fd_ci_jac; | |
| 700 | |
| 701 if (iscell (__sqp_cif__) && length (__sqp_cif__) > 1) | |
| 702 cigradfcn = __sqp_cif__{2}; | |
| 703 endif | |
|
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704 |
|
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705 if (isempty (cigradfcn)) |
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706 res = bgrad; |
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707 else |
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Rik <octave@nomad.inbox5.com>
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708 res = [feval(cigradfcn,x); bgrad]; |
| 6768 | 709 endif |
| 710 | |
| 7399 | 711 endfunction |
| 7361 | 712 |
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713 # Utility function used to debug sqp |
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714 function report (iter, qp_iter, alpha, nfun, obj) |
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parents:
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715 |
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716 if (nargin == 0) |
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717 printf (" Itn ItQP Step Nfun Objective\n"); |
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718 else |
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719 printf ("%5d %4d %8.1g %5d %13.6e\n", iter, qp_iter, alpha, nfun, obj); |
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720 endif |
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721 |
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722 endfunction |
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723 |
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724 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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725 %% Test Code |
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726 |
| 7371 | 727 %!function r = g (x) |
| 728 %! r = [sumsq(x)-10; | |
| 729 %! x(2)*x(3)-5*x(4)*x(5); | |
| 730 %! x(1)^3+x(2)^3+1 ]; | |
| 7361 | 731 %! |
| 7371 | 732 %!function obj = phi (x) |
| 733 %! obj = exp(prod(x)) - 0.5*(x(1)^3+x(2)^3+1)^2; | |
| 7361 | 734 %! |
| 735 %!test | |
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736 %! |
| 7361 | 737 %! x0 = [-1.8; 1.7; 1.9; -0.8; -0.8]; |
| 738 %! | |
| 7381 | 739 %! [x, obj, info, iter, nf, lambda] = sqp (x0, @phi, @g, []); |
| 7361 | 740 %! |
| 741 %! x_opt = [-1.717143501952599; | |
| 742 %! 1.595709610928535; | |
| 743 %! 1.827245880097156; | |
| 744 %! -0.763643103133572; | |
| 745 %! -0.763643068453300]; | |
| 746 %! | |
| 7371 | 747 %! obj_opt = 0.0539498477702739; |
| 7361 | 748 %! |
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8047
d54f113aa983
Increase test script tolerances.
Thomas Treichl <Thomas.Treichl@gmx.net>
parents:
7795
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749 %! assert (all (abs (x-x_opt) < 5*sqrt (eps)) && abs (obj-obj_opt) < sqrt (eps)); |
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750 |
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751 %% Test input validation |
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752 %!error sqp () |
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753 %!error sqp (1) |
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754 %!error sqp (1,2,3,4,5,6,7,8,9) |
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755 %!error sqp (1,2,3,4,5) |
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756 %!error sqp (ones(2,2)) |
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757 %!error sqp (1,cell(4,1)) |
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758 %!error sqp (1,cell(3,1),cell(3,1)) |
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759 %!error sqp (1,cell(3,1),cell(2,1),cell(3,1)) |
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760 %!error sqp (1,cell(3,1),cell(2,1),cell(2,1),ones(2,2),[]) |
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761 %!error sqp (1,cell(3,1),cell(2,1),cell(2,1),[],ones(2,2)) |
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parents:
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762 %!error sqp (1,cell(3,1),cell(2,1),cell(2,1),1,-1) |
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parents:
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763 %!error sqp (1,cell(3,1),cell(2,1),cell(2,1),[],[],ones(2,2)) |
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Rik <octave@nomad.inbox5.com>
parents:
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764 %!error sqp (1,cell(3,1),cell(2,1),cell(2,1),[],[],-1) |
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Rik <octave@nomad.inbox5.com>
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765 %!error sqp (1,cell(3,1),cell(2,1),cell(2,1),[],[],1.5) |
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766 %!error sqp (1,cell(3,1),cell(2,1),cell(2,1),[],[],[],ones(2,2)) |
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parents:
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767 %!error sqp (1,cell(3,1),cell(2,1),cell(2,1),[],[],[],-1) |