Mercurial > hg > octave-nkf
annotate scripts/optimization/sqp.m @ 9665:1dba57e9d08d
use blas_trans_type for xgemm
| author | Jaroslav Hajek <highegg@gmail.com> |
|---|---|
| date | Sat, 26 Sep 2009 10:41:07 +0200 |
| parents | 16f53d29049f |
| children | 952d4df5b686 |
| rev | line source |
|---|---|
| 9245 | 1 ## Copyright (C) 2005, 2006, 2007, 2008, 2009 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{x}, @var{phi}, @var{g}, @var{h}, @var{lb}, @var{ub}, @var{maxiter}, @var{tolerance}) |
| 5289 | 21 ## Solve the nonlinear program |
| 6741 | 22 ## @tex |
| 23 ## $$ | |
| 24 ## \min_x \phi (x) | |
| 25 ## $$ | |
| 26 ## @end tex | |
| 27 ## @ifnottex | |
| 5289 | 28 ## |
| 29 ## @example | |
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30 ## @group |
| 5289 | 31 ## min phi (x) |
| 32 ## x | |
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33 ## @end group |
| 5289 | 34 ## @end example |
| 35 ## | |
| 6741 | 36 ## @end ifnottex |
| 37 ## subject to | |
| 5289 | 38 ## @tex |
| 6741 | 39 ## $$ |
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40 ## g(x) = 0 \qquad h(x) \geq 0 \qquad lb \leq x \leq ub |
| 6741 | 41 ## $$ |
| 5289 | 42 ## @end tex |
| 6741 | 43 ## @ifnottex |
| 5289 | 44 ## |
| 45 ## @example | |
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46 ## @group |
| 5289 | 47 ## g(x) = 0 |
| 48 ## h(x) >= 0 | |
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49 ## lb <= x <= ub |
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50 ## @end group |
| 5289 | 51 ## @end example |
| 6741 | 52 ## @end ifnottex |
| 5289 | 53 ## |
| 54 ## @noindent | |
| 55 ## using a successive quadratic programming method. | |
| 56 ## | |
| 57 ## The first argument is the initial guess for the vector @var{x}. | |
| 58 ## | |
| 7001 | 59 ## The second argument is a function handle pointing to the objective |
| 5289 | 60 ## function. The objective function must be of the form |
| 61 ## | |
| 62 ## @example | |
| 63 ## y = phi (x) | |
| 64 ## @end example | |
| 65 ## | |
| 66 ## @noindent | |
| 67 ## in which @var{x} is a vector and @var{y} is a scalar. | |
| 68 ## | |
| 69 ## The second argument may also be a 2- or 3-element cell array of | |
| 70 ## function handles. The first element should point to the objective | |
| 71 ## function, the second should point to a function that computes the | |
| 72 ## gradient of the objective function, and the third should point to a | |
| 73 ## function to compute the hessian of the objective function. If the | |
| 74 ## gradient function is not supplied, the gradient is computed by finite | |
| 75 ## differences. If the hessian function is not supplied, a BFGS update | |
| 76 ## formula is used to approximate the hessian. | |
| 77 ## | |
| 78 ## If supplied, the gradient function must be of the form | |
| 79 ## | |
| 80 ## @example | |
| 7031 | 81 ## g = gradient (x) |
| 5289 | 82 ## @end example |
| 83 ## | |
| 84 ## @noindent | |
| 85 ## in which @var{x} is a vector and @var{g} is a vector. | |
| 86 ## | |
| 87 ## If supplied, the hessian function must be of the form | |
| 88 ## | |
| 89 ## @example | |
| 7031 | 90 ## h = hessian (x) |
| 5289 | 91 ## @end example |
| 92 ## | |
| 93 ## @noindent | |
| 94 ## in which @var{x} is a vector and @var{h} is a matrix. | |
| 95 ## | |
| 96 ## The third and fourth arguments are function handles pointing to | |
| 97 ## functions that compute the equality constraints and the inequality | |
| 98 ## constraints, respectively. | |
| 99 ## | |
| 100 ## If your problem does not have equality (or inequality) constraints, | |
| 101 ## you may pass an empty matrix for @var{cef} (or @var{cif}). | |
| 102 ## | |
| 103 ## If supplied, the equality and inequality constraint functions must be | |
| 104 ## of the form | |
| 105 ## | |
| 106 ## @example | |
| 7031 | 107 ## r = f (x) |
| 5289 | 108 ## @end example |
| 109 ## | |
| 110 ## @noindent | |
| 111 ## in which @var{x} is a vector and @var{r} is a vector. | |
| 112 ## | |
| 113 ## The third and fourth arguments may also be 2-element cell arrays of | |
| 114 ## function handles. The first element should point to the constraint | |
| 115 ## function and the second should point to a function that computes the | |
| 116 ## gradient of the constraint function: | |
| 117 ## | |
| 6741 | 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 ## @ifnottex | |
| 5289 | 126 ## @example |
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127 ## @group |
| 5289 | 128 ## [ d f(x) d f(x) d f(x) ] |
| 129 ## transpose ( [ ------ ----- ... ------ ] ) | |
| 130 ## [ dx_1 dx_2 dx_N ] | |
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131 ## @end group |
| 5289 | 132 ## @end example |
| 6741 | 133 ## @end ifnottex |
| 5289 | 134 ## |
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135 ## The fifth and sixth arguments are vectors containing lower and upper bounds |
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136 ## on @var{x}. These must be consistent with equality and inequality |
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137 ## constraints @var{g} and @var{h}. If the bounds are not specified, or are |
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138 ## empty, they are set to -@var{realmax} and @var{realmax} by default. |
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139 ## |
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140 ## The seventh argument is max. number of iterations. If not specified, |
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141 ## the default value is 100. |
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142 ## |
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143 ## The eighth argument is tolerance for stopping criteria. If not specified, |
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144 ## the default value is @var{eps}. |
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145 ## |
| 5289 | 146 ## Here is an example of calling @code{sqp}: |
| 147 ## | |
| 148 ## @example | |
| 7031 | 149 ## function r = g (x) |
| 150 ## r = [ sumsq(x)-10; | |
| 151 ## x(2)*x(3)-5*x(4)*x(5); | |
| 152 ## x(1)^3+x(2)^3+1 ]; | |
| 153 ## endfunction | |
| 154 ## | |
| 155 ## function obj = phi (x) | |
| 156 ## obj = exp(prod(x)) - 0.5*(x(1)^3+x(2)^3+1)^2; | |
| 157 ## endfunction | |
| 5289 | 158 ## |
| 7031 | 159 ## x0 = [-1.8; 1.7; 1.9; -0.8; -0.8]; |
| 160 ## | |
| 161 ## [x, obj, info, iter, nf, lambda] = sqp (x0, @@phi, @@g, []) | |
| 5289 | 162 ## |
| 7031 | 163 ## x = |
| 164 ## | |
| 165 ## -1.71714 | |
| 166 ## 1.59571 | |
| 167 ## 1.82725 | |
| 168 ## -0.76364 | |
| 169 ## -0.76364 | |
| 5289 | 170 ## |
| 7031 | 171 ## obj = 0.053950 |
| 172 ## info = 101 | |
| 173 ## iter = 8 | |
| 174 ## nf = 10 | |
| 175 ## lambda = | |
| 176 ## | |
| 177 ## -0.0401627 | |
| 178 ## 0.0379578 | |
| 179 ## -0.0052227 | |
| 5289 | 180 ## @end example |
| 181 ## | |
| 182 ## The value returned in @var{info} may be one of the following: | |
| 183 ## @table @asis | |
| 184 ## @item 101 | |
| 185 ## The algorithm terminated because the norm of the last step was less | |
| 186 ## than @code{tol * norm (x))} (the value of tol is currently fixed at | |
| 187 ## @code{sqrt (eps)}---edit @file{sqp.m} to modify this value. | |
| 188 ## @item 102 | |
| 189 ## The BFGS update failed. | |
| 190 ## @item 103 | |
| 191 ## The maximum number of iterations was reached (the maximum number of | |
| 192 ## allowed iterations is currently fixed at 100---edit @file{sqp.m} to | |
| 193 ## increase this value). | |
| 194 ## @end table | |
| 5642 | 195 ## @seealso{qp} |
| 5289 | 196 ## @end deftypefn |
| 197 | |
| 6768 | 198 function [x, obj, info, iter, nf, lambda] = sqp (x, objf, cef, cif, lb, ub, maxiter, tolerance) |
| 5289 | 199 |
| 6768 | 200 global __sqp_nfun__; |
| 5289 | 201 global __sqp_obj_fun__; |
| 202 global __sqp_ce_fun__; | |
| 203 global __sqp_ci_fun__; | |
| 6768 | 204 global __sqp_cif__; |
| 205 global __sqp_cifcn__; | |
| 5289 | 206 |
| 6768 | 207 if (nargin >= 2 && nargin <= 8 && nargin != 5) |
| 5289 | 208 |
| 209 ## Choose an initial NxN symmetric positive definite Hessan | |
| 210 ## approximation B. | |
| 211 | |
| 212 n = length (x); | |
| 213 | |
| 214 ## Evaluate objective function, constraints, and gradients at initial | |
| 215 ## value of x. | |
| 216 ## | |
| 217 ## obj_fun | |
| 218 ## obj_grad | |
| 219 ## ce_fun -- equality constraint functions | |
| 220 ## ci_fun -- inequality constraint functions | |
| 221 ## A == [grad_{x_1} cx_fun, grad_{x_2} cx_fun, ..., grad_{x_n} cx_fun]^T | |
| 222 | |
| 223 obj_grd = @fd_obj_grd; | |
| 224 have_hess = 0; | |
| 225 if (iscell (objf)) | |
| 226 if (length (objf) > 0) | |
| 227 __sqp_obj_fun__ = obj_fun = objf{1}; | |
| 228 if (length (objf) > 1) | |
| 229 obj_grd = objf{2}; | |
| 230 if (length (objf) > 2) | |
| 231 obj_hess = objf{3}; | |
| 232 have_hess = 1; | |
| 233 endif | |
| 234 endif | |
| 235 else | |
| 236 error ("sqp: invalid objective function"); | |
| 237 endif | |
| 238 else | |
| 239 __sqp_obj_fun__ = obj_fun = objf; | |
| 240 endif | |
| 241 | |
| 242 ce_fun = @empty_cf; | |
| 243 ce_grd = @empty_jac; | |
| 244 if (nargin > 2) | |
| 245 ce_grd = @fd_ce_jac; | |
| 246 if (iscell (cef)) | |
| 247 if (length (cef) > 0) | |
| 248 __sqp_ce_fun__ = ce_fun = cef{1}; | |
| 249 if (length (cef) > 1) | |
| 250 ce_grd = cef{2}; | |
| 251 endif | |
| 252 else | |
| 253 error ("sqp: invalid equality constraint function"); | |
| 254 endif | |
| 255 elseif (! isempty (cef)) | |
| 256 ce_fun = cef; | |
| 257 endif | |
| 258 endif | |
| 259 __sqp_ce_fun__ = ce_fun; | |
| 260 | |
| 261 ci_fun = @empty_cf; | |
| 262 ci_grd = @empty_jac; | |
| 6768 | 263 |
| 5289 | 264 if (nargin > 3) |
| 6768 | 265 ## constraint function given by user with possibly gradient |
| 266 __sqp_cif__ = cif; | |
| 267 ## constraint function given by user without gradient | |
| 268 __sqp_cifcn__ = @empty_cf; | |
| 269 if (iscell (__sqp_cif__)) | |
| 270 if (length (__sqp_cif__) > 0) | |
| 271 __sqp_cifcn__ = __sqp_cif__{1}; | |
| 272 endif | |
| 273 elseif (! isempty (__sqp_cif__)) | |
| 274 __sqp_cifcn__ = __sqp_cif__; | |
| 275 endif | |
| 276 | |
| 277 if (nargin < 5) | |
| 278 ci_grd = @fd_ci_jac; | |
| 279 if (iscell (cif)) | |
| 280 if (length (cif) > 0) | |
| 281 __sqp_ci_fun__ = ci_fun = cif{1}; | |
| 282 if (length (cif) > 1) | |
| 283 ci_grd = cif{2}; | |
| 284 endif | |
| 285 else | |
| 286 error ("sqp: invalid equality constraint function"); | |
| 5289 | 287 endif |
| 6768 | 288 elseif (! isempty (cif)) |
| 289 ci_fun = cif; | |
| 290 endif | |
| 291 else | |
| 292 global __sqp_lb__; | |
| 293 if (isvector (lb)) | |
| 294 __sqp_lb__ = lb; | |
| 295 elseif (isempty (lb)) | |
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296 if (isa (x, "single")) |
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297 __sqp_lb__ = -realmax ("single"); |
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298 else |
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299 __sqp_lb__ = -realmax; |
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300 endif |
| 5289 | 301 else |
| 6768 | 302 error ("sqp: invalid lower bound"); |
| 5289 | 303 endif |
| 6768 | 304 |
| 305 global __sqp_ub__; | |
| 306 if (isvector (ub)) | |
| 307 __sqp_ub__ = ub; | |
| 308 elseif (isempty (lb)) | |
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309 if (isa (x, "single")) |
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310 __sqp_ub__ = realmax ("single"); |
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311 else |
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312 __sqp_ub__ = realmax; |
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313 endif |
| 6768 | 314 else |
| 315 error ("sqp: invalid upper bound"); | |
| 316 endif | |
| 317 | |
| 318 if (lb > ub) | |
| 319 error ("sqp: upper bound smaller than lower bound"); | |
| 320 endif | |
| 321 __sqp_ci_fun__ = ci_fun = @cf_ub_lb; | |
| 322 ci_grd = @cigrad_ub_lb; | |
| 323 endif | |
| 324 __sqp_ci_fun__ = ci_fun; | |
| 325 endif | |
| 326 | |
| 327 iter_max = 100; | |
| 328 if (nargin > 6 && ! isempty (maxiter)) | |
| 6921 | 329 if (isscalar (maxiter) && maxiter > 0 && round (maxiter) == maxiter) |
| 6768 | 330 iter_max = maxiter; |
| 331 else | |
| 332 error ("sqp: invalid number of maximum iterations"); | |
| 5289 | 333 endif |
| 334 endif | |
| 335 | |
| 6768 | 336 tol = sqrt (eps); |
| 337 if (nargin > 7 && ! isempty (tolerance)) | |
| 338 if (isscalar (tolerance) && tolerance > 0) | |
| 339 tol = tolerance; | |
| 340 else | |
| 341 error ("sqp: invalid value for tolerance"); | |
| 342 endif | |
| 343 endif | |
| 5289 | 344 |
| 345 iter = 0; | |
| 346 | |
| 347 obj = feval (obj_fun, x); | |
| 6768 | 348 __sqp_nfun__ = 1; |
| 5289 | 349 |
| 350 c = feval (obj_grd, x); | |
| 351 | |
| 6382 | 352 if (have_hess) |
| 353 B = feval (obj_hess, x); | |
| 354 else | |
| 355 B = eye (n, n); | |
| 356 endif | |
| 357 | |
| 5289 | 358 ce = feval (ce_fun, x); |
| 359 F = feval (ce_grd, x); | |
| 360 | |
| 361 ci = feval (ci_fun, x); | |
| 362 C = feval (ci_grd, x); | |
| 363 | |
| 364 A = [F; C]; | |
| 365 | |
| 366 ## Choose an initial lambda (x is provided by the caller). | |
| 367 | |
| 368 lambda = 100 * ones (rows (A), 1); | |
| 369 | |
| 370 qp_iter = 1; | |
| 371 alpha = 1; | |
| 372 | |
| 373 ## report (); | |
| 374 | |
| 6768 | 375 ## report (iter, qp_iter, alpha, __sqp_nfun__, obj); |
| 5289 | 376 |
| 6527 | 377 info = 0; |
| 378 | |
| 5289 | 379 while (++iter < iter_max) |
| 380 | |
| 381 ## Check convergence. This is just a simple check on the first | |
| 382 ## order necessary conditions. | |
| 383 | |
| 384 ## IDX is the indices of the active inequality constraints. | |
| 385 | |
| 386 nr_f = rows (F); | |
| 387 | |
| 388 lambda_e = lambda((1:nr_f)'); | |
| 389 lambda_i = lambda((nr_f+1:end)'); | |
| 390 | |
| 391 con = [ce; ci]; | |
| 392 | |
| 393 t0 = norm (c - A' * lambda); | |
| 394 t1 = norm (ce); | |
| 395 t2 = all (ci >= 0); | |
| 396 t3 = all (lambda_i >= 0); | |
| 397 t4 = norm (lambda .* con); | |
| 398 | |
| 399 if (t2 && t3 && max ([t0; t1; t4]) < tol) | |
| 400 break; | |
| 401 endif | |
| 402 | |
| 403 ## Compute search direction p by solving QP. | |
| 404 | |
| 405 g = -ce; | |
| 406 d = -ci; | |
| 407 | |
| 408 ## Discard inequality constraints that have -Inf bounds since those | |
| 409 ## will never be active. | |
| 410 idx = isinf (d) & d < 0; | |
| 411 d(idx) = []; | |
| 412 C(idx,:) = []; | |
| 413 | |
| 414 [p, obj_qp, INFO, lambda] = qp (x, B, c, F, g, [], [], d, C, | |
| 415 Inf * ones (size (d))); | |
| 416 | |
| 417 info = INFO.info; | |
| 418 | |
| 419 ## Check QP solution and attempt to recover if it has failed. | |
| 420 | |
| 421 ## Choose mu such that p is a descent direction for the chosen | |
| 422 ## merit function phi. | |
| 423 | |
| 424 [x_new, alpha, obj_new] = linesearch_L1 (x, p, obj_fun, obj_grd, | |
| 425 ce_fun, ci_fun, lambda, obj); | |
| 426 | |
| 427 ## Evaluate objective function, constraints, and gradients at | |
| 428 ## x_new. | |
| 429 | |
| 430 c_new = feval (obj_grd, x_new); | |
| 431 | |
| 432 ce_new = feval (ce_fun, x_new); | |
| 433 F_new = feval (ce_grd, x_new); | |
| 434 | |
| 435 ci_new = feval (ci_fun, x_new); | |
| 436 C_new = feval (ci_grd, x_new); | |
| 437 | |
| 438 A_new = [F_new; C_new]; | |
| 439 | |
| 440 ## Set | |
| 441 ## | |
| 442 ## s = alpha * p | |
| 443 ## y = grad_x L (x_new, lambda) - grad_x L (x, lambda}) | |
| 444 | |
| 445 y = c_new - c; | |
| 446 | |
| 447 if (! isempty (A)) | |
| 448 t = ((A_new - A)'*lambda); | |
| 449 y -= t; | |
| 450 endif | |
| 451 | |
| 452 delx = x_new - x; | |
| 453 | |
| 454 if (norm (delx) < tol * norm (x)) | |
| 455 info = 101; | |
| 456 break; | |
| 457 endif | |
| 458 | |
| 459 if (have_hess) | |
| 460 | |
| 461 B = feval (obj_hess, x); | |
| 462 | |
| 463 else | |
| 464 | |
| 465 ## Update B using a quasi-Newton formula. | |
| 466 | |
| 467 delxt = delx'; | |
| 468 | |
| 469 ## Damped BFGS. Or maybe we would actually want to use the Hessian | |
| 470 ## of the Lagrangian, computed directly. | |
| 471 | |
| 472 d1 = delxt*B*delx; | |
| 473 | |
| 474 t1 = 0.2 * d1; | |
| 475 t2 = delxt*y; | |
| 476 | |
| 477 if (t2 < t1) | |
| 478 theta = 0.8*d1/(d1 - t2); | |
| 479 else | |
| 480 theta = 1; | |
| 481 endif | |
| 482 | |
| 483 r = theta*y + (1-theta)*B*delx; | |
| 484 | |
| 485 d2 = delxt*r; | |
| 486 | |
| 487 if (d1 == 0 || d2 == 0) | |
| 488 info = 102; | |
| 489 break; | |
| 490 endif | |
| 491 | |
| 492 B = B - B*delx*delxt*B/d1 + r*r'/d2; | |
| 493 | |
| 494 endif | |
| 495 | |
| 496 x = x_new; | |
| 497 | |
| 498 obj = obj_new; | |
| 499 | |
| 500 c = c_new; | |
| 501 | |
| 502 ce = ce_new; | |
| 503 F = F_new; | |
| 504 | |
| 505 ci = ci_new; | |
| 506 C = C_new; | |
| 507 | |
| 508 A = A_new; | |
| 509 | |
| 6768 | 510 ## report (iter, qp_iter, alpha, __sqp_nfun__, obj); |
| 5289 | 511 |
| 512 endwhile | |
| 513 | |
| 514 if (iter >= iter_max) | |
| 515 info = 103; | |
| 516 endif | |
| 517 | |
| 6768 | 518 nf = __sqp_nfun__; |
| 5289 | 519 |
| 520 else | |
| 521 | |
| 6046 | 522 print_usage (); |
| 5289 | 523 |
| 524 endif | |
| 525 | |
| 7399 | 526 endfunction |
| 5289 | 527 |
| 528 | |
| 529 function [merit, obj] = phi_L1 (obj, obj_fun, ce_fun, ci_fun, x, mu) | |
| 530 | |
| 6768 | 531 global __sqp_nfun__; |
| 5289 | 532 |
| 533 ce = feval (ce_fun, x); | |
| 534 ci = feval (ci_fun, x); | |
| 535 | |
| 536 idx = ci < 0; | |
| 537 | |
| 538 con = [ce; ci(idx)]; | |
| 539 | |
| 540 if (isempty (obj)) | |
| 541 obj = feval (obj_fun, x); | |
| 6768 | 542 __sqp_nfun__++; |
| 5289 | 543 endif |
| 544 | |
| 545 merit = obj; | |
| 546 t = norm (con, 1) / mu; | |
| 547 | |
| 548 if (! isempty (t)) | |
| 549 merit += t; | |
| 550 endif | |
| 551 | |
| 7399 | 552 endfunction |
| 5289 | 553 |
| 554 | |
| 555 function [x_new, alpha, obj] = linesearch_L1 (x, p, obj_fun, obj_grd, | |
| 556 ce_fun, ci_fun, lambda, obj) | |
| 557 | |
| 558 ## Choose parameters | |
| 559 ## | |
| 560 ## eta in the range (0, 0.5) | |
| 561 ## tau in the range (0, 1) | |
| 562 | |
| 563 eta = 0.25; | |
| 564 tau = 0.5; | |
| 565 | |
| 566 delta_bar = sqrt (eps); | |
| 567 | |
| 568 if (isempty (lambda)) | |
| 569 mu = 1 / delta_bar; | |
| 570 else | |
| 571 mu = 1 / (norm (lambda, Inf) + delta_bar); | |
| 572 endif | |
| 573 | |
| 574 alpha = 1; | |
| 575 | |
| 576 c = feval (obj_grd, x); | |
| 577 ce = feval (ce_fun, x); | |
| 578 | |
| 579 [phi_x_mu, obj] = phi_L1 (obj, obj_fun, ce_fun, ci_fun, x, mu); | |
| 580 | |
| 581 D_phi_x_mu = c' * p; | |
| 582 d = feval (ci_fun, x); | |
| 583 ## only those elements of d corresponding | |
| 584 ## to violated constraints should be included. | |
| 585 idx = d < 0; | |
| 586 t = - norm ([ce; d(idx)], 1) / mu; | |
| 587 if (! isempty (t)) | |
| 588 D_phi_x_mu += t; | |
| 589 endif | |
| 590 | |
| 591 while (1) | |
| 592 [p1, obj] = phi_L1 ([], obj_fun, ce_fun, ci_fun, x+alpha*p, mu); | |
| 593 p2 = phi_x_mu+eta*alpha*D_phi_x_mu; | |
| 594 if (p1 > p2) | |
| 595 ## Reset alpha = tau_alpha * alpha for some tau_alpha in the | |
| 596 ## range (0, tau). | |
| 597 tau_alpha = 0.9 * tau; ## ?? | |
| 598 alpha = tau_alpha * alpha; | |
| 599 else | |
| 600 break; | |
| 601 endif | |
| 602 endwhile | |
| 603 | |
| 604 ## Set x_new = x + alpha * p; | |
| 605 | |
| 606 x_new = x + alpha * p; | |
| 607 | |
| 7399 | 608 endfunction |
| 5289 | 609 |
| 610 | |
| 611 function report (iter, qp_iter, alpha, nfun, obj) | |
| 612 | |
| 613 if (nargin == 0) | |
| 614 printf (" Itn ItQP Step Nfun Objective\n"); | |
| 615 else | |
| 616 printf ("%5d %4d %8.1g %5d %13.6e\n", iter, qp_iter, alpha, nfun, obj); | |
| 617 endif | |
| 618 | |
| 7399 | 619 endfunction |
| 5289 | 620 |
| 621 | |
| 622 function grd = fdgrd (f, x) | |
| 623 | |
| 624 if (! isempty (f)) | |
| 625 y0 = feval (f, x); | |
| 626 nx = length (x); | |
| 627 grd = zeros (nx, 1); | |
| 628 deltax = sqrt (eps); | |
| 629 for i = 1:nx | |
| 630 t = x(i); | |
| 631 x(i) += deltax; | |
| 632 grd(i) = (feval (f, x) - y0) / deltax; | |
| 633 x(i) = t; | |
| 634 endfor | |
| 635 else | |
| 636 grd = zeros (0, 1); | |
| 637 endif | |
| 638 | |
| 7399 | 639 endfunction |
| 5289 | 640 |
| 641 | |
| 642 function jac = fdjac (f, x) | |
| 6768 | 643 nx = length (x); |
| 5289 | 644 if (! isempty (f)) |
| 645 y0 = feval (f, x); | |
| 646 nf = length (y0); | |
| 647 nx = length (x); | |
| 648 jac = zeros (nf, nx); | |
| 649 deltax = sqrt (eps); | |
| 650 for i = 1:nx | |
| 651 t = x(i); | |
| 652 x(i) += deltax; | |
| 653 jac(:,i) = (feval (f, x) - y0) / deltax; | |
| 654 x(i) = t; | |
| 655 endfor | |
| 656 else | |
| 657 jac = zeros (0, nx); | |
| 658 endif | |
| 659 | |
| 7399 | 660 endfunction |
| 5289 | 661 |
| 662 | |
| 663 function grd = fd_obj_grd (x) | |
| 664 | |
| 665 global __sqp_obj_fun__; | |
| 666 | |
| 667 grd = fdgrd (__sqp_obj_fun__, x); | |
| 668 | |
| 7399 | 669 endfunction |
| 5289 | 670 |
| 671 | |
| 672 function res = empty_cf (x) | |
| 673 | |
| 674 res = zeros (0, 1); | |
| 675 | |
| 7399 | 676 endfunction |
| 5289 | 677 |
| 678 | |
| 679 function res = empty_jac (x) | |
| 680 | |
| 681 res = zeros (0, length (x)); | |
| 682 | |
| 7399 | 683 endfunction |
| 5289 | 684 |
| 685 | |
| 686 function jac = fd_ce_jac (x) | |
| 687 | |
| 688 global __sqp_ce_fun__; | |
| 689 | |
| 690 jac = fdjac (__sqp_ce_fun__, x); | |
| 691 | |
| 7399 | 692 endfunction |
| 5289 | 693 |
| 694 | |
| 695 function jac = fd_ci_jac (x) | |
| 696 | |
| 6768 | 697 global __sqp_cifcn__; |
| 698 ## __sqp_cifcn__ = constraint function without gradients and lb or ub | |
| 699 jac = fdjac (__sqp_cifcn__, x); | |
| 700 | |
| 7399 | 701 endfunction |
| 6768 | 702 |
| 7017 | 703 |
| 6768 | 704 function res = cf_ub_lb (x) |
| 5289 | 705 |
| 6768 | 706 ## combine constraint function with ub and lb |
| 707 global __sqp_cifcn__ __sqp_lb__ __sqp_ub__ | |
| 708 | |
| 709 res = [x-__sqp_lb__; __sqp_ub__-x]; | |
| 710 | |
| 711 if (! isempty (__sqp_cifcn__)) | |
| 712 res = [feval(__sqp_cifcn__,x); x-__sqp_lb__; __sqp_ub__-x]; | |
| 713 endif | |
| 5289 | 714 |
| 7399 | 715 endfunction |
| 6768 | 716 |
| 7017 | 717 |
| 6768 | 718 function res = cigrad_ub_lb (x) |
| 719 | |
| 720 global __sqp_cif__ | |
| 721 | |
| 722 res = [eye(numel(x)); -eye(numel(x))]; | |
| 723 | |
| 724 cigradfcn = @fd_ci_jac; | |
| 725 | |
| 726 if (iscell (__sqp_cif__) && length (__sqp_cif__) > 1) | |
| 727 cigradfcn = __sqp_cif__{2}; | |
| 728 endif | |
| 729 | |
| 730 if (! isempty (cigradfcn)) | |
| 731 res = [feval(cigradfcn,x); eye(numel(x)); -eye(numel(x))]; | |
| 732 endif | |
| 733 | |
| 7399 | 734 endfunction |
| 7361 | 735 |
| 7371 | 736 %!function r = g (x) |
| 737 %! r = [sumsq(x)-10; | |
| 738 %! x(2)*x(3)-5*x(4)*x(5); | |
| 739 %! x(1)^3+x(2)^3+1 ]; | |
| 7361 | 740 %! |
| 7371 | 741 %!function obj = phi (x) |
| 742 %! obj = exp(prod(x)) - 0.5*(x(1)^3+x(2)^3+1)^2; | |
| 7361 | 743 %! |
| 744 %!test | |
| 745 %! x0 = [-1.8; 1.7; 1.9; -0.8; -0.8]; | |
| 746 %! | |
| 7381 | 747 %! [x, obj, info, iter, nf, lambda] = sqp (x0, @phi, @g, []); |
| 7361 | 748 %! |
| 749 %! x_opt = [-1.717143501952599; | |
| 750 %! 1.595709610928535; | |
| 751 %! 1.827245880097156; | |
| 752 %! -0.763643103133572; | |
| 753 %! -0.763643068453300]; | |
| 754 %! | |
| 7371 | 755 %! obj_opt = 0.0539498477702739; |
| 7361 | 756 %! |
|
8047
d54f113aa983
Increase test script tolerances.
Thomas Treichl <Thomas.Treichl@gmx.net>
parents:
7795
diff
changeset
|
757 %! assert (all (abs (x-x_opt) < 5*sqrt (eps)) && abs (obj-obj_opt) < sqrt (eps)); |