Mercurial > hg > octave-lyh
annotate scripts/optimization/sqp.m @ 11290:646063a22a35
sqp.m: Use correct stopping tolerance in documentation.
| author | Rik <octave@nomad.inbox5.com> |
|---|---|
| date | Mon, 22 Nov 2010 19:07:48 -0800 |
| parents | a44f979a35ce |
| children | 2726132f77f6 |
| 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}) |
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21 ## @deftypefnx {Function File} {[@dots{}] =} sqp (@var{x}, @var{phi}, @var{g}) |
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22 ## @deftypefnx {Function File} {[@dots{}] =} sqp (@var{x}, @var{phi}, @var{g}, @var{h}) |
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23 ## @deftypefnx {Function File} {[@dots{}] =} sqp (@var{x}, @var{phi}, @var{g}, @var{h}, @var{lb}, @var{ub}) |
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24 ## @deftypefnx {Function File} {[@dots{}] =} sqp (@var{x}, @var{phi}, @var{g}, @var{h}, @var{lb}, @var{ub}, @var{maxiter}) |
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25 ## @deftypefnx {Function File} {[@dots{}] =} sqp (@var{x}, @var{phi}, @var{g}, @var{h}, @var{lb}, @var{ub}, @var{maxiter}, @var{tolerance}) |
| 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 |
| 60 ## using a successive quadratic programming method. | |
| 61 ## | |
| 62 ## The first argument is the initial guess for the vector @var{x}. | |
| 63 ## | |
| 7001 | 64 ## The second argument is a function handle pointing to the objective |
| 5289 | 65 ## function. The objective function must be of the form |
| 66 ## | |
| 67 ## @example | |
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68 ## @var{y} = phi (@var{x}) |
| 5289 | 69 ## @end example |
| 70 ## | |
| 71 ## @noindent | |
| 72 ## in which @var{x} is a vector and @var{y} is a scalar. | |
| 73 ## | |
| 74 ## The second argument may also be a 2- or 3-element cell array of | |
| 75 ## function handles. The first element should point to the objective | |
| 76 ## function, the second should point to a function that computes the | |
| 77 ## gradient of the objective function, and the third should point to a | |
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78 ## function that computes the Hessian of the objective function. If the |
| 5289 | 79 ## gradient function is not supplied, the gradient is computed by finite |
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80 ## differences. If the Hessian function is not supplied, a BFGS update |
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81 ## formula is used to approximate the Hessian. |
| 5289 | 82 ## |
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83 ## When supplied, the gradient function must be of the form |
| 5289 | 84 ## |
| 85 ## @example | |
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86 ## @var{g} = gradient (@var{x}) |
| 5289 | 87 ## @end example |
| 88 ## | |
| 89 ## @noindent | |
| 90 ## in which @var{x} is a vector and @var{g} is a vector. | |
| 91 ## | |
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92 ## When supplied, the Hessian function must be of the form |
| 5289 | 93 ## |
| 94 ## @example | |
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95 ## @var{h} = hessian (@var{x}) |
| 5289 | 96 ## @end example |
| 97 ## | |
| 98 ## @noindent | |
| 99 ## in which @var{x} is a vector and @var{h} is a matrix. | |
| 100 ## | |
| 101 ## The third and fourth arguments are function handles pointing to | |
| 102 ## functions that compute the equality constraints and the inequality | |
| 103 ## constraints, respectively. | |
| 104 ## | |
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105 ## If the problem does not have equality (or inequality) constraints, |
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106 ## then use an empty matrix ([]) for @var{cef} (or @var{cif}). |
| 5289 | 107 ## |
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108 ## When supplied, the equality and inequality constraint functions must be |
| 5289 | 109 ## of the form |
| 110 ## | |
| 111 ## @example | |
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112 ## @var{r} = f (@var{x}) |
| 5289 | 113 ## @end example |
| 114 ## | |
| 115 ## @noindent | |
| 116 ## in which @var{x} is a vector and @var{r} is a vector. | |
| 117 ## | |
| 118 ## The third and fourth arguments may also be 2-element cell arrays of | |
| 119 ## function handles. The first element should point to the constraint | |
| 120 ## function and the second should point to a function that computes the | |
| 121 ## gradient of the constraint function: | |
| 6741 | 122 ## @tex |
| 123 ## $$ | |
| 124 ## \Bigg( {\partial f(x) \over \partial x_1}, | |
| 125 ## {\partial f(x) \over \partial x_2}, \ldots, | |
| 126 ## {\partial f(x) \over \partial x_N} \Bigg)^T | |
| 127 ## $$ | |
| 128 ## @end tex | |
| 129 ## @ifnottex | |
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130 ## |
| 5289 | 131 ## @example |
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132 ## @group |
| 5289 | 133 ## [ d f(x) d f(x) d f(x) ] |
| 134 ## transpose ( [ ------ ----- ... ------ ] ) | |
| 135 ## [ dx_1 dx_2 dx_N ] | |
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136 ## @end group |
| 5289 | 137 ## @end example |
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138 ## |
| 6741 | 139 ## @end ifnottex |
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140 ## The fifth and sixth arguments contain lower and upper bounds |
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141 ## on @var{x}. These must be consistent with the equality and inequality |
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142 ## constraints @var{g} and @var{h}. If the arguments are vectors then |
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143 ## @var{x}(i) is bound by @var{lb}(i) and @var{ub}(i). A bound can also |
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144 ## be a scalar in which case all elements of @var{x} will share the same |
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145 ## bound. If only one bound (lb, ub) is specified then the other will |
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146 ## default to (-@var{realmax}, +@var{realmax}). |
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147 ## |
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148 ## The seventh argument specifies the maximum number of iterations. |
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149 ## The default value is 100. |
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150 ## |
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151 ## The eighth argument specifies the tolerance for the stopping criteria. |
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152 ## The default value is @code{sqrt(eps)}. |
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153 ## |
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154 ## The value returned in @var{info} may be one of the following: |
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155 ## |
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156 ## @table @asis |
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157 ## @item 101 |
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158 ## The algorithm terminated normally. |
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159 ## Either all constraints meet the requested tolerance, or the stepsize, |
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160 ## @tex |
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161 ## $\Delta x,$ |
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162 ## @end tex |
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163 ## @ifnottex |
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164 ## delta @var{x}, |
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165 ## @end ifnottex |
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166 ## is less than @code{tol * norm (x)}. |
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167 ## |
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168 ## @item 102 |
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169 ## The BFGS update failed. |
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170 ## |
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171 ## @item 103 |
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172 ## The maximum number of iterations was reached. |
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173 ## @end table |
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174 ## |
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175 ## An example of calling @code{sqp}: |
| 5289 | 176 ## |
| 177 ## @example | |
| 7031 | 178 ## function r = g (x) |
| 179 ## r = [ sumsq(x)-10; | |
| 180 ## x(2)*x(3)-5*x(4)*x(5); | |
| 181 ## x(1)^3+x(2)^3+1 ]; | |
| 182 ## endfunction | |
| 183 ## | |
| 184 ## function obj = phi (x) | |
| 185 ## obj = exp(prod(x)) - 0.5*(x(1)^3+x(2)^3+1)^2; | |
| 186 ## endfunction | |
| 5289 | 187 ## |
| 7031 | 188 ## x0 = [-1.8; 1.7; 1.9; -0.8; -0.8]; |
| 189 ## | |
| 190 ## [x, obj, info, iter, nf, lambda] = sqp (x0, @@phi, @@g, []) | |
| 5289 | 191 ## |
| 7031 | 192 ## x = |
| 193 ## | |
| 194 ## -1.71714 | |
| 195 ## 1.59571 | |
| 196 ## 1.82725 | |
| 197 ## -0.76364 | |
| 198 ## -0.76364 | |
| 5289 | 199 ## |
| 7031 | 200 ## obj = 0.053950 |
| 201 ## info = 101 | |
| 202 ## iter = 8 | |
| 203 ## nf = 10 | |
| 204 ## lambda = | |
| 205 ## | |
| 206 ## -0.0401627 | |
| 207 ## 0.0379578 | |
| 208 ## -0.0052227 | |
| 5289 | 209 ## @end example |
| 210 ## | |
| 5642 | 211 ## @seealso{qp} |
| 5289 | 212 ## @end deftypefn |
| 213 | |
| 6768 | 214 function [x, obj, info, iter, nf, lambda] = sqp (x, objf, cef, cif, lb, ub, maxiter, tolerance) |
| 5289 | 215 |
| 6768 | 216 global __sqp_nfun__; |
| 5289 | 217 global __sqp_obj_fun__; |
| 218 global __sqp_ce_fun__; | |
| 219 global __sqp_ci_fun__; | |
| 6768 | 220 global __sqp_cif__; |
| 221 global __sqp_cifcn__; | |
| 5289 | 222 |
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223 if (nargin < 2 || nargin > 8 || nargin == 5) |
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224 print_usage (); |
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225 endif |
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227 if (!isvector (x)) |
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228 error ("sqp: X must be a vector"); |
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229 endif |
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230 if (rows (x) == 1) |
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231 x = x'; |
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232 endif |
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234 obj_grd = @fd_obj_grd; |
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235 have_hess = 0; |
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236 if (iscell (objf)) |
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237 switch (numel (objf)) |
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238 case 1 |
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239 obj_fun = objf{1}; |
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240 case 2 |
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241 obj_fun = objf{1}; |
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242 obj_grd = objf{2}; |
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243 case 3 |
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244 obj_fun = objf{1}; |
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245 obj_grd = objf{2}; |
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246 obj_hess = objf{3}; |
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247 have_hess = 1; |
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248 otherwise |
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249 error ("sqp: invalid objective function specification"); |
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250 endswitch |
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251 else |
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252 obj_fun = objf; # No cell array, only obj_fun set |
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253 endif |
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254 __sqp_obj_fun__ = obj_fun; |
| 5289 | 255 |
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256 ce_fun = @empty_cf; |
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257 ce_grd = @empty_jac; |
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258 if (nargin > 2) |
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259 ce_grd = @fd_ce_jac; |
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260 if (iscell (cef)) |
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261 switch (numel (cef)) |
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262 case 1 |
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263 ce_fun = cef{1}; |
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264 case 2 |
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265 ce_fun = cef{1}; |
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266 ce_grd = cef{2}; |
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267 otherwise |
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268 error ("sqp: invalid equality constraint function specification"); |
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269 endswitch |
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270 elseif (! isempty (cef)) |
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271 ce_fun = cef; # No cell array, only constraint equality function set |
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272 endif |
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273 endif |
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274 __sqp_ce_fun__ = ce_fun; |
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275 |
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276 ci_fun = @empty_cf; |
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277 ci_grd = @empty_jac; |
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278 if (nargin > 3) |
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279 ## constraint function given by user with possible gradient |
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280 __sqp_cif__ = cif; |
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281 ## constraint function given by user without gradient |
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282 __sqp_cifcn__ = @empty_cf; |
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283 if (iscell (cif)) |
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284 if (length (cif) > 0) |
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285 __sqp_cifcn__ = cif{1}; |
| 5289 | 286 endif |
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287 elseif (! isempty (cif)) |
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288 __sqp_cifcn__ = cif; |
| 5289 | 289 endif |
| 290 | |
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291 if (nargin < 5 || (nargin > 5 && isempty (lb) && isempty (ub))) |
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292 ## constraint inequality function only without any bounds |
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293 ci_grd = @fd_ci_jac; |
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294 if (iscell (cif)) |
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295 switch length (cif) |
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296 case {1} |
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297 ci_fun = cif{1}; |
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298 case {2} |
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299 ci_fun = cif{1}; |
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300 ci_grd = cif{2}; |
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301 otherwise |
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302 error ("sqp: invalid inequality constraint function specification"); |
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303 endswitch |
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304 elseif (! isempty (cif)) |
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305 ci_fun = cif; # No cell array, only constraint inequality function set |
| 5289 | 306 endif |
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307 else |
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308 ## constraint inequality function with bounds present |
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309 global __sqp_lb__; |
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310 if (isvector (lb)) |
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311 __sqp_lb__ = lb(:); |
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312 elseif (isempty (lb)) |
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313 if (isa (x, "single")) |
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314 __sqp_lb__ = -realmax ("single"); |
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315 else |
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316 __sqp_lb__ = -realmax; |
| 10549 | 317 endif |
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318 else |
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319 error ("sqp: invalid lower bound"); |
| 6768 | 320 endif |
| 321 | |
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322 global __sqp_ub__; |
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323 if (isvector (ub)) |
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324 __sqp_ub__ = ub(:); |
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325 elseif (isempty (ub)) |
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326 if (isa (x, "single")) |
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327 __sqp_ub__ = realmax ("single"); |
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328 else |
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329 __sqp_ub__ = realmax; |
| 10549 | 330 endif |
| 6768 | 331 else |
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332 error ("sqp: invalid upper bound"); |
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333 endif |
| 6768 | 334 |
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335 if (__sqp_lb__ > __sqp_ub__) |
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336 error ("sqp: upper bound smaller than lower bound"); |
| 6768 | 337 endif |
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338 ci_fun = @cf_ub_lb; |
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339 ci_grd = @cigrad_ub_lb; |
| 6768 | 340 endif |
| 5289 | 341 |
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342 __sqp_ci_fun__ = ci_fun; |
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343 endif # if (nargin > 3) |
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344 |
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345 iter_max = 100; |
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346 if (nargin > 6 && ! isempty (maxiter)) |
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347 if (isscalar (maxiter) && maxiter > 0 && fix (maxiter) == maxiter) |
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348 iter_max = maxiter; |
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349 else |
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350 error ("sqp: invalid number of maximum iterations"); |
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351 endif |
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352 endif |
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353 |
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354 tol = sqrt (eps); |
|
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355 if (nargin > 7 && ! isempty (tolerance)) |
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356 if (isscalar (tolerance) && tolerance > 0) |
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357 tol = tolerance; |
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358 else |
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359 error ("sqp: invalid value for tolerance"); |
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360 endif |
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361 endif |
| 5289 | 362 |
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363 ## Evaluate objective function, constraints, and gradients at initial |
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364 ## value of x. |
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365 ## |
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366 ## obj_fun -- objective function |
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367 ## obj_grad -- objective gradient |
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368 ## ce_fun -- equality constraint functions |
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369 ## ci_fun -- inequality constraint functions |
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370 ## A == [grad_{x_1} cx_fun, grad_{x_2} cx_fun, ..., grad_{x_n} cx_fun]^T |
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371 |
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372 obj = feval (obj_fun, x); |
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373 __sqp_nfun__ = 1; |
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374 |
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375 c = feval (obj_grd, x); |
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376 |
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377 ## Choose an initial NxN symmetric positive definite Hessan |
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378 ## approximation B. |
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379 n = length (x); |
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380 if (have_hess) |
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381 B = feval (obj_hess, x); |
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382 else |
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383 B = eye (n, n); |
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384 endif |
| 5289 | 385 |
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386 ce = feval (ce_fun, x); |
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387 F = feval (ce_grd, x); |
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388 |
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389 ci = feval (ci_fun, x); |
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390 C = feval (ci_grd, x); |
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391 |
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392 A = [F; C]; |
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393 |
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394 ## Choose an initial lambda (x is provided by the caller). |
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395 |
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396 lambda = 100 * ones (rows (A), 1); |
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397 |
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398 qp_iter = 1; |
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399 alpha = 1; |
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400 |
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401 # report (); |
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402 |
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403 # report (iter, qp_iter, alpha, __sqp_nfun__, obj); |
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404 |
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405 info = 0; |
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406 iter = 0; |
| 5289 | 407 |
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408 while (++iter < iter_max) |
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409 |
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410 ## Check convergence. This is just a simple check on the first |
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411 ## order necessary conditions. |
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412 |
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413 ## idx is the indices of the active inequality constraints. |
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414 |
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415 nr_f = rows (F); |
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416 |
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417 lambda_e = lambda((1:nr_f)'); |
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418 lambda_i = lambda((nr_f+1:end)'); |
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419 |
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420 con = [ce; ci]; |
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421 |
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422 t0 = norm (c - A' * lambda); |
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423 t1 = norm (ce); |
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424 t2 = all (ci >= 0); |
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425 t3 = all (lambda_i >= 0); |
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426 t4 = norm (lambda .* con); |
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427 |
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428 if (t2 && t3 && max ([t0; t1; t4]) < tol) |
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429 info = 101; |
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430 break; |
| 6382 | 431 endif |
| 432 | |
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433 ## Compute search direction p by solving QP. |
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434 |
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435 g = -ce; |
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436 d = -ci; |
| 5289 | 437 |
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438 ## Discard inequality constraints that have -Inf bounds since those |
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439 ## will never be active. |
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440 idx = isinf (d) & d < 0; |
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441 d(idx) = []; |
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442 C(idx,:) = []; |
| 5289 | 443 |
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444 [p, obj_qp, INFO, lambda] = qp (x, B, c, F, g, [], [], d, C, |
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445 Inf (size (d))); |
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446 |
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447 info = INFO.info; |
| 5289 | 448 |
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449 ## Check QP solution and attempt to recover if it has failed. |
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450 |
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451 ## Choose mu such that p is a descent direction for the chosen |
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452 ## merit function phi. |
| 5289 | 453 |
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454 [x_new, alpha, obj_new] = linesearch_L1 (x, p, obj_fun, obj_grd, |
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455 ce_fun, ci_fun, lambda, obj); |
| 5289 | 456 |
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457 ## Evaluate objective function, constraints, and gradients at |
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458 ## x_new. |
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459 |
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460 c_new = feval (obj_grd, x_new); |
| 5289 | 461 |
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462 ce_new = feval (ce_fun, x_new); |
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463 F_new = feval (ce_grd, x_new); |
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464 |
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465 ci_new = feval (ci_fun, x_new); |
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466 C_new = feval (ci_grd, x_new); |
| 5289 | 467 |
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468 A_new = [F_new; C_new]; |
| 5289 | 469 |
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470 ## Set |
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471 ## |
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472 ## s = alpha * p |
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473 ## y = grad_x L (x_new, lambda) - grad_x L (x, lambda}) |
| 6527 | 474 |
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475 y = c_new - c; |
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476 |
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477 if (! isempty (A)) |
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478 t = ((A_new - A)'*lambda); |
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479 y -= t; |
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480 endif |
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481 |
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482 delx = x_new - x; |
| 5289 | 483 |
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484 if (norm (delx) < tol * norm (x)) |
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485 info = 101; |
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486 break; |
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487 endif |
| 5289 | 488 |
|
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489 if (have_hess) |
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490 |
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491 B = feval (obj_hess, x); |
| 5289 | 492 |
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493 else |
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494 |
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495 ## Update B using a quasi-Newton formula. |
| 5289 | 496 |
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497 delxt = delx'; |
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498 |
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499 ## Damped BFGS. Or maybe we would actually want to use the Hessian |
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500 ## of the Lagrangian, computed directly. |
| 5289 | 501 |
|
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502 d1 = delxt*B*delx; |
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503 |
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504 t1 = 0.2 * d1; |
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505 t2 = delxt*y; |
| 5289 | 506 |
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507 if (t2 < t1) |
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508 theta = 0.8*d1/(d1 - t2); |
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509 else |
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510 theta = 1; |
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511 endif |
| 5289 | 512 |
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513 r = theta*y + (1-theta)*B*delx; |
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514 |
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515 d2 = delxt*r; |
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516 |
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517 if (d1 == 0 || d2 == 0) |
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518 info = 102; |
| 10549 | 519 break; |
| 5289 | 520 endif |
| 521 | |
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522 B = B - B*delx*delxt*B/d1 + r*r'/d2; |
| 5289 | 523 |
| 524 endif | |
| 525 | |
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526 x = x_new; |
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527 |
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528 obj = obj_new; |
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529 |
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530 c = c_new; |
| 5289 | 531 |
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532 ce = ce_new; |
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533 F = F_new; |
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534 |
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535 ci = ci_new; |
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536 C = C_new; |
| 5289 | 537 |
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538 A = A_new; |
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539 |
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540 # report (iter, qp_iter, alpha, __sqp_nfun__, obj); |
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541 |
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542 endwhile |
| 5289 | 543 |
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544 if (iter >= iter_max) |
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545 info = 103; |
| 5289 | 546 endif |
| 547 | |
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548 nf = __sqp_nfun__; |
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549 |
| 7399 | 550 endfunction |
| 5289 | 551 |
| 552 | |
| 553 function [merit, obj] = phi_L1 (obj, obj_fun, ce_fun, ci_fun, x, mu) | |
| 554 | |
| 6768 | 555 global __sqp_nfun__; |
| 5289 | 556 |
| 557 ce = feval (ce_fun, x); | |
| 558 ci = feval (ci_fun, x); | |
| 559 | |
| 560 idx = ci < 0; | |
| 561 | |
| 562 con = [ce; ci(idx)]; | |
| 563 | |
| 564 if (isempty (obj)) | |
| 565 obj = feval (obj_fun, x); | |
| 6768 | 566 __sqp_nfun__++; |
| 5289 | 567 endif |
| 568 | |
| 569 merit = obj; | |
| 570 t = norm (con, 1) / mu; | |
| 571 | |
| 572 if (! isempty (t)) | |
| 573 merit += t; | |
| 574 endif | |
| 575 | |
| 7399 | 576 endfunction |
| 5289 | 577 |
| 578 | |
| 579 function [x_new, alpha, obj] = linesearch_L1 (x, p, obj_fun, obj_grd, | |
| 10549 | 580 ce_fun, ci_fun, lambda, obj) |
| 5289 | 581 |
| 582 ## Choose parameters | |
| 583 ## | |
| 584 ## eta in the range (0, 0.5) | |
| 585 ## tau in the range (0, 1) | |
| 586 | |
| 587 eta = 0.25; | |
| 588 tau = 0.5; | |
| 589 | |
| 590 delta_bar = sqrt (eps); | |
| 591 | |
| 592 if (isempty (lambda)) | |
| 593 mu = 1 / delta_bar; | |
| 594 else | |
| 595 mu = 1 / (norm (lambda, Inf) + delta_bar); | |
| 596 endif | |
| 597 | |
| 598 alpha = 1; | |
| 599 | |
| 600 c = feval (obj_grd, x); | |
| 601 ce = feval (ce_fun, x); | |
| 602 | |
| 603 [phi_x_mu, obj] = phi_L1 (obj, obj_fun, ce_fun, ci_fun, x, mu); | |
| 604 | |
| 605 D_phi_x_mu = c' * p; | |
| 606 d = feval (ci_fun, x); | |
| 607 ## only those elements of d corresponding | |
| 608 ## to violated constraints should be included. | |
| 609 idx = d < 0; | |
| 610 t = - norm ([ce; d(idx)], 1) / mu; | |
| 611 if (! isempty (t)) | |
| 612 D_phi_x_mu += t; | |
| 613 endif | |
| 614 | |
| 615 while (1) | |
| 616 [p1, obj] = phi_L1 ([], obj_fun, ce_fun, ci_fun, x+alpha*p, mu); | |
| 617 p2 = phi_x_mu+eta*alpha*D_phi_x_mu; | |
| 618 if (p1 > p2) | |
| 619 ## Reset alpha = tau_alpha * alpha for some tau_alpha in the | |
| 620 ## range (0, tau). | |
|
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621 tau_alpha = 0.9 * tau; # ?? |
| 5289 | 622 alpha = tau_alpha * alpha; |
| 623 else | |
| 624 break; | |
| 625 endif | |
| 626 endwhile | |
| 627 | |
| 628 x_new = x + alpha * p; | |
| 629 | |
| 7399 | 630 endfunction |
| 5289 | 631 |
| 632 | |
| 633 function report (iter, qp_iter, alpha, nfun, obj) | |
| 634 | |
| 635 if (nargin == 0) | |
| 636 printf (" Itn ItQP Step Nfun Objective\n"); | |
| 637 else | |
| 638 printf ("%5d %4d %8.1g %5d %13.6e\n", iter, qp_iter, alpha, nfun, obj); | |
| 639 endif | |
| 640 | |
| 7399 | 641 endfunction |
| 5289 | 642 |
| 643 | |
| 644 function grd = fdgrd (f, x) | |
| 645 | |
| 646 if (! isempty (f)) | |
| 647 y0 = feval (f, x); | |
| 648 nx = length (x); | |
| 649 grd = zeros (nx, 1); | |
| 650 deltax = sqrt (eps); | |
| 651 for i = 1:nx | |
| 652 t = x(i); | |
| 653 x(i) += deltax; | |
| 654 grd(i) = (feval (f, x) - y0) / deltax; | |
| 655 x(i) = t; | |
| 656 endfor | |
| 657 else | |
| 658 grd = zeros (0, 1); | |
| 659 endif | |
| 660 | |
| 7399 | 661 endfunction |
| 5289 | 662 |
| 663 | |
| 664 function jac = fdjac (f, x) | |
| 6768 | 665 nx = length (x); |
| 5289 | 666 if (! isempty (f)) |
| 667 y0 = feval (f, x); | |
| 668 nf = length (y0); | |
| 669 nx = length (x); | |
| 670 jac = zeros (nf, nx); | |
| 671 deltax = sqrt (eps); | |
| 672 for i = 1:nx | |
| 673 t = x(i); | |
| 674 x(i) += deltax; | |
| 675 jac(:,i) = (feval (f, x) - y0) / deltax; | |
| 676 x(i) = t; | |
| 677 endfor | |
| 678 else | |
| 679 jac = zeros (0, nx); | |
| 680 endif | |
| 681 | |
| 7399 | 682 endfunction |
| 5289 | 683 |
| 684 | |
| 685 function grd = fd_obj_grd (x) | |
| 686 | |
| 687 global __sqp_obj_fun__; | |
| 688 | |
| 689 grd = fdgrd (__sqp_obj_fun__, x); | |
| 690 | |
| 7399 | 691 endfunction |
| 5289 | 692 |
| 693 | |
| 694 function res = empty_cf (x) | |
| 695 | |
| 696 res = zeros (0, 1); | |
| 697 | |
| 7399 | 698 endfunction |
| 5289 | 699 |
| 700 | |
| 701 function res = empty_jac (x) | |
| 702 | |
| 703 res = zeros (0, length (x)); | |
| 704 | |
| 7399 | 705 endfunction |
| 5289 | 706 |
| 707 | |
| 708 function jac = fd_ce_jac (x) | |
| 709 | |
| 710 global __sqp_ce_fun__; | |
| 711 | |
| 712 jac = fdjac (__sqp_ce_fun__, x); | |
| 713 | |
| 7399 | 714 endfunction |
| 5289 | 715 |
| 716 | |
| 717 function jac = fd_ci_jac (x) | |
| 718 | |
| 6768 | 719 global __sqp_cifcn__; |
| 720 ## __sqp_cifcn__ = constraint function without gradients and lb or ub | |
| 721 jac = fdjac (__sqp_cifcn__, x); | |
| 722 | |
| 7399 | 723 endfunction |
| 6768 | 724 |
| 7017 | 725 |
| 6768 | 726 function res = cf_ub_lb (x) |
| 5289 | 727 |
| 6768 | 728 ## combine constraint function with ub and lb |
| 729 global __sqp_cifcn__ __sqp_lb__ __sqp_ub__ | |
| 730 | |
| 731 res = [x-__sqp_lb__; __sqp_ub__-x]; | |
| 732 | |
| 733 if (! isempty (__sqp_cifcn__)) | |
| 734 res = [feval(__sqp_cifcn__,x); x-__sqp_lb__; __sqp_ub__-x]; | |
| 735 endif | |
| 5289 | 736 |
| 7399 | 737 endfunction |
| 6768 | 738 |
| 7017 | 739 |
| 6768 | 740 function res = cigrad_ub_lb (x) |
| 741 | |
| 742 global __sqp_cif__ | |
| 743 | |
| 744 res = [eye(numel(x)); -eye(numel(x))]; | |
| 745 | |
| 746 cigradfcn = @fd_ci_jac; | |
| 747 | |
| 748 if (iscell (__sqp_cif__) && length (__sqp_cif__) > 1) | |
| 749 cigradfcn = __sqp_cif__{2}; | |
| 750 endif | |
| 10549 | 751 |
| 6768 | 752 if (! isempty (cigradfcn)) |
| 753 res = [feval(cigradfcn,x); eye(numel(x)); -eye(numel(x))]; | |
| 754 endif | |
| 755 | |
| 7399 | 756 endfunction |
| 7361 | 757 |
| 7371 | 758 %!function r = g (x) |
| 759 %! r = [sumsq(x)-10; | |
| 760 %! x(2)*x(3)-5*x(4)*x(5); | |
| 761 %! x(1)^3+x(2)^3+1 ]; | |
| 7361 | 762 %! |
| 7371 | 763 %!function obj = phi (x) |
| 764 %! obj = exp(prod(x)) - 0.5*(x(1)^3+x(2)^3+1)^2; | |
| 7361 | 765 %! |
| 766 %!test | |
|
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767 %! |
| 7361 | 768 %! x0 = [-1.8; 1.7; 1.9; -0.8; -0.8]; |
| 769 %! | |
| 7381 | 770 %! [x, obj, info, iter, nf, lambda] = sqp (x0, @phi, @g, []); |
| 7361 | 771 %! |
| 772 %! x_opt = [-1.717143501952599; | |
| 773 %! 1.595709610928535; | |
| 774 %! 1.827245880097156; | |
| 775 %! -0.763643103133572; | |
| 776 %! -0.763643068453300]; | |
| 777 %! | |
| 7371 | 778 %! obj_opt = 0.0539498477702739; |
| 7361 | 779 %! |
|
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780 %! assert (all (abs (x-x_opt) < 5*sqrt (eps)) && abs (obj-obj_opt) < sqrt (eps)); |
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781 |
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782 %% Test input validation |
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783 %!error sqp () |
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784 %!error sqp (1) |
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785 %!error sqp (1,2,3,4,5,6,7,8,9) |
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786 %!error sqp (1,2,3,4,5) |
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787 %!error sqp (ones(2,2)) |
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788 %!error sqp (1,cell(4,1)) |
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789 %!error sqp (1,cell(3,1),cell(3,1)) |
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790 %!error sqp (1,cell(3,1),cell(2,1),cell(3,1)) |
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Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents:
10549
diff
changeset
|
791 %!error sqp (1,cell(3,1),cell(2,1),cell(2,1),ones(2,2),[]) |
|
35338deff753
Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents:
10549
diff
changeset
|
792 %!error sqp (1,cell(3,1),cell(2,1),cell(2,1),[],ones(2,2)) |
|
35338deff753
Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents:
10549
diff
changeset
|
793 %!error sqp (1,cell(3,1),cell(2,1),cell(2,1),1,-1) |
|
35338deff753
Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents:
10549
diff
changeset
|
794 %!error sqp (1,cell(3,1),cell(2,1),cell(2,1),[],[],ones(2,2)) |
|
35338deff753
Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents:
10549
diff
changeset
|
795 %!error sqp (1,cell(3,1),cell(2,1),cell(2,1),[],[],-1) |
|
35338deff753
Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents:
10549
diff
changeset
|
796 %!error sqp (1,cell(3,1),cell(2,1),cell(2,1),[],[],1.5) |
|
35338deff753
Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents:
10549
diff
changeset
|
797 %!error sqp (1,cell(3,1),cell(2,1),cell(2,1),[],[],[],ones(2,2)) |
|
35338deff753
Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents:
10549
diff
changeset
|
798 %!error sqp (1,cell(3,1),cell(2,1),cell(2,1),[],[],[],-1) |