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annotate scripts/optimization/sqp.m @ 14363:f3d52523cde1
Use Octave coding conventions in all m-file %!test blocks
* wavread.m, acosd.m, acot.m, acotd.m, acoth.m, acsc.m, acscd.m, acsch.m,
asec.m, asecd.m, asech.m, asind.m, atand.m, cosd.m, cot.m, cotd.m, coth.m,
csc.m, cscd.m, csch.m, sec.m, secd.m, sech.m, sind.m, tand.m, accumarray.m,
accumdim.m, bitcmp.m, bitget.m, bitset.m, blkdiag.m, cart2pol.m, cart2sph.m,
celldisp.m, chop.m, circshift.m, colon.m, common_size.m, cplxpair.m,
cumtrapz.m, curl.m, dblquad.m, deal.m, divergence.m, flipdim.m, fliplr.m,
flipud.m, genvarname.m, gradient.m, idivide.m, int2str.m, interp1.m,
interp1q.m, interp2.m, interp3.m, interpft.m, interpn.m, isa.m, isdir.m,
isequal.m, isequalwithequalnans.m, issquare.m, logspace.m, nargchk.m,
narginchk.m, nargoutchk.m, nextpow2.m, nthargout.m, num2str.m, pol2cart.m,
polyarea.m, postpad.m, prepad.m, profile.m, profshow.m, quadgk.m, quadv.m,
randi.m, rat.m, repmat.m, rot90.m, rotdim.m, shift.m, shiftdim.m, sph2cart.m,
structfun.m, trapz.m, triplequad.m, convhull.m, dsearch.m, dsearchn.m,
griddata3.m, griddatan.m, rectint.m, tsearchn.m, __makeinfo__.m, doc.m,
get_first_help_sentence.m, help.m, type.m, unimplemented.m, which.m, imread.m,
imwrite.m, dlmwrite.m, fileread.m, is_valid_file_id.m, strread.m, textread.m,
textscan.m, commutation_matrix.m, cond.m, condest.m, cross.m,
duplication_matrix.m, expm.m, housh.m, isdefinite.m, ishermitian.m,
issymmetric.m, logm.m, normest.m, null.m, onenormest.m, orth.m, planerot.m,
qzhess.m, rank.m, rref.m, trace.m, vech.m, ans.m, bincoeff.m, bug_report.m,
bzip2.m, comma.m, compare_versions.m, computer.m, edit.m, fileparts.m,
fullfile.m, getfield.m, gzip.m, info.m, inputname.m, isappdata.m, isdeployed.m,
ismac.m, ispc.m, isunix.m, list_primes.m, ls.m, mexext.m, namelengthmax.m,
news.m, orderfields.m, paren.m, recycle.m, rmappdata.m, semicolon.m,
setappdata.m, setfield.m, substruct.m, symvar.m, ver.m, version.m,
warning_ids.m, xor.m, fminbnd.m, fsolve.m, fzero.m, lsqnonneg.m, optimset.m,
pqpnonneg.m, sqp.m, matlabroot.m, __gnuplot_drawnow__.m,
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ginput.m, graphics_toolkit.m, gtext.m, hggroup.m, hist.m, hold.m, isfigure.m,
ishghandle.m, ishold.m, isocolors.m, isonormals.m, isosurface.m, isprop.m,
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fftshift.m, freqz.m, hamming.m, hanning.m, ifftshift.m, sinc.m, sinetone.m,
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median.m, mode.m, moment.m, ols.m, ppplot.m, prctile.m, probit.m, quantile.m,
range.m, ranks.m, run_count.m, runlength.m, skewness.m, spearman.m,
statistics.m, std.m, table.m, var.m, zscore.m, betacdf.m, betainv.m, betapdf.m,
betarnd.m, binocdf.m, binoinv.m, binopdf.m, binornd.m, cauchy_cdf.m,
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chi2rnd.m, discrete_cdf.m, discrete_inv.m, discrete_pdf.m, discrete_rnd.m,
empirical_cdf.m, empirical_inv.m, empirical_pdf.m, empirical_rnd.m, expcdf.m,
expinv.m, exppdf.m, exprnd.m, fcdf.m, finv.m, fpdf.m, frnd.m, gamcdf.m,
gaminv.m, gampdf.m, gamrnd.m, geocdf.m, geoinv.m, geopdf.m, geornd.m,
hygecdf.m, hygeinv.m, hygepdf.m, hygernd.m, kolmogorov_smirnov_cdf.m,
laplace_cdf.m, laplace_inv.m, laplace_pdf.m, laplace_rnd.m, logistic_cdf.m,
logistic_inv.m, logistic_pdf.m, logistic_rnd.m, logncdf.m, logninv.m,
lognpdf.m, lognrnd.m, nbincdf.m, nbininv.m, nbinpdf.m, nbinrnd.m, normcdf.m,
norminv.m, normpdf.m, normrnd.m, poisscdf.m, poissinv.m, poisspdf.m,
poissrnd.m, stdnormal_cdf.m, stdnormal_inv.m, stdnormal_pdf.m, stdnormal_rnd.m,
tcdf.m, tinv.m, tpdf.m, trnd.m, unidcdf.m, unidinv.m, unidpdf.m, unidrnd.m,
unifcdf.m, unifinv.m, unifpdf.m, unifrnd.m, wblcdf.m, wblinv.m, wblpdf.m,
wblrnd.m, kolmogorov_smirnov_test.m, kruskal_wallis_test.m, base2dec.m,
bin2dec.m, blanks.m, cstrcat.m, deblank.m, dec2base.m, dec2bin.m, dec2hex.m,
findstr.m, hex2dec.m, index.m, isletter.m, mat2str.m, rindex.m, str2num.m,
strcat.m, strjust.m, strmatch.m, strsplit.m, strtok.m, strtrim.m, strtrunc.m,
substr.m, validatestring.m, demo.m, example.m, fail.m, speed.m, addtodate.m,
asctime.m, clock.m, ctime.m, date.m, datenum.m, datetick.m, datevec.m,
eomday.m, etime.m, is_leap_year.m, now.m:
Use Octave coding conventions in all m-file %!test blocks
| author | Rik <octave@nomad.inbox5.com> |
|---|---|
| date | Mon, 13 Feb 2012 07:29:44 -0800 |
| parents | 4d917a6a858b |
| children | 86854d032a37 |
| rev | line source |
|---|---|
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1 ## Copyright (C) 2005-2012 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 |
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36 ## min phi (x) |
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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 |
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52 ## g(x) = 0 |
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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 supplied, 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 |
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105 ## [ d f(x) d f(x) d f(x) ] |
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106 ## transpose ( [ ------ ----- ... ------ ] ) |
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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) | |
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158 ## obj = exp (prod (x)) - 0.5*(x(1)^3+x(2)^3+1)^2; |
| 7031 | 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 ## FIXME -- check QP solution and attempt to recover if it has |
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420 ## failed. For now, just warn about possible problems. |
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421 |
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422 id = "Octave:SQP-QP-subproblem"; |
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423 switch (info) |
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424 case 2 |
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425 warning (id, "sqp: QP subproblem is non-convex and unbounded"); |
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426 case 3 |
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427 warning (id, "sqp: QP subproblem failed to converge in %d iterations", |
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428 INFO.solveiter); |
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429 case 6 |
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430 warning (id, "sqp: QP subproblem is infeasible"); |
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431 endswitch |
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432 |
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433 ## Choose mu such that p is a descent direction for the chosen |
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434 ## merit function phi. |
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435 [x_new, alpha, obj_new] = linesearch_L1 (x, p, obj_fun, obj_grd, |
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436 ce_fun, ci_fun, lambda, obj); |
| 5289 | 437 |
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438 ## Evaluate objective function, constraints, and gradients at x_new. |
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439 c_new = feval (obj_grd, x_new); |
| 5289 | 440 |
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441 ce_new = feval (ce_fun, x_new); |
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442 F_new = feval (ce_grd, x_new); |
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443 |
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444 ci_new = feval (ci_fun, x_new); |
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445 C_new = feval (ci_grd, x_new); |
| 5289 | 446 |
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447 A_new = [F_new; C_new]; |
| 5289 | 448 |
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449 ## Set |
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450 ## |
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451 ## s = alpha * p |
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452 ## y = grad_x L (x_new, lambda) - grad_x L (x, lambda}) |
| 6527 | 453 |
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454 y = c_new - c; |
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455 |
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456 if (! isempty (A)) |
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457 t = ((A_new - A)'*lambda); |
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458 y -= t; |
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459 endif |
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460 |
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461 delx = x_new - x; |
| 5289 | 462 |
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463 if (norm (delx) < tol * norm (x)) |
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464 info = 101; |
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465 break; |
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466 endif |
| 5289 | 467 |
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468 if (have_hess) |
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469 |
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470 B = feval (obj_hess, x); |
| 5289 | 471 |
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472 else |
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473 ## Update B using a quasi-Newton formula. |
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474 delxt = delx'; |
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475 |
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476 ## Damped BFGS. Or maybe we would actually want to use the Hessian |
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477 ## of the Lagrangian, computed directly? |
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478 d1 = delxt*B*delx; |
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479 |
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480 t1 = 0.2 * d1; |
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481 t2 = delxt*y; |
| 5289 | 482 |
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483 if (t2 < t1) |
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484 theta = 0.8*d1/(d1 - t2); |
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485 else |
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486 theta = 1; |
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487 endif |
| 5289 | 488 |
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489 r = theta*y + (1-theta)*B*delx; |
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490 |
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491 d2 = delxt*r; |
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492 |
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493 if (d1 == 0 || d2 == 0) |
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494 info = 102; |
| 10549 | 495 break; |
| 5289 | 496 endif |
| 497 | |
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498 B = B - B*delx*delxt*B/d1 + r*r'/d2; |
| 5289 | 499 |
| 500 endif | |
| 501 | |
|
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502 x = x_new; |
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503 |
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504 obj = obj_new; |
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505 |
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506 c = c_new; |
| 5289 | 507 |
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508 ce = ce_new; |
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509 F = F_new; |
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510 |
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511 ci = ci_new; |
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512 C = C_new; |
| 5289 | 513 |
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514 A = A_new; |
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515 |
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516 # report (iter, qp_iter, alpha, __sqp_nfun__, obj); |
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517 |
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518 endwhile |
| 5289 | 519 |
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520 if (iter >= iter_max) |
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521 info = 103; |
| 5289 | 522 endif |
| 523 | |
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524 nf = __sqp_nfun__; |
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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, | |
| 10549 | 556 ce_fun, ci_fun, lambda, obj) |
| 5289 | 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). | |
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597 tau_alpha = 0.9 * tau; # ?? |
| 5289 | 598 alpha = tau_alpha * alpha; |
| 599 else | |
| 600 break; | |
| 601 endif | |
| 602 endwhile | |
| 603 | |
| 604 x_new = x + alpha * p; | |
| 605 | |
| 7399 | 606 endfunction |
| 5289 | 607 |
| 608 | |
| 609 function grd = fdgrd (f, x) | |
| 610 | |
| 611 if (! isempty (f)) | |
| 612 y0 = feval (f, x); | |
| 613 nx = length (x); | |
| 614 grd = zeros (nx, 1); | |
| 615 deltax = sqrt (eps); | |
| 616 for i = 1:nx | |
| 617 t = x(i); | |
| 618 x(i) += deltax; | |
| 619 grd(i) = (feval (f, x) - y0) / deltax; | |
| 620 x(i) = t; | |
| 621 endfor | |
| 622 else | |
| 623 grd = zeros (0, 1); | |
| 624 endif | |
| 625 | |
| 7399 | 626 endfunction |
| 5289 | 627 |
| 628 | |
| 629 function jac = fdjac (f, x) | |
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630 |
| 6768 | 631 nx = length (x); |
| 5289 | 632 if (! isempty (f)) |
| 633 y0 = feval (f, x); | |
| 634 nf = length (y0); | |
| 635 nx = length (x); | |
| 636 jac = zeros (nf, nx); | |
| 637 deltax = sqrt (eps); | |
| 638 for i = 1:nx | |
| 639 t = x(i); | |
| 640 x(i) += deltax; | |
| 641 jac(:,i) = (feval (f, x) - y0) / deltax; | |
| 642 x(i) = t; | |
| 643 endfor | |
| 644 else | |
| 645 jac = zeros (0, nx); | |
| 646 endif | |
| 647 | |
| 7399 | 648 endfunction |
| 5289 | 649 |
| 650 | |
| 651 function grd = fd_obj_grd (x) | |
| 652 | |
| 653 global __sqp_obj_fun__; | |
| 654 | |
| 655 grd = fdgrd (__sqp_obj_fun__, x); | |
| 656 | |
| 7399 | 657 endfunction |
| 5289 | 658 |
| 659 | |
| 660 function res = empty_cf (x) | |
| 661 | |
| 662 res = zeros (0, 1); | |
| 663 | |
| 7399 | 664 endfunction |
| 5289 | 665 |
| 666 | |
| 667 function res = empty_jac (x) | |
| 668 | |
| 669 res = zeros (0, length (x)); | |
| 670 | |
| 7399 | 671 endfunction |
| 5289 | 672 |
| 673 | |
| 674 function jac = fd_ce_jac (x) | |
| 675 | |
| 676 global __sqp_ce_fun__; | |
| 677 | |
| 678 jac = fdjac (__sqp_ce_fun__, x); | |
| 679 | |
| 7399 | 680 endfunction |
| 5289 | 681 |
| 682 | |
| 683 function jac = fd_ci_jac (x) | |
| 684 | |
| 6768 | 685 global __sqp_cifcn__; |
| 686 ## __sqp_cifcn__ = constraint function without gradients and lb or ub | |
| 687 jac = fdjac (__sqp_cifcn__, x); | |
| 688 | |
| 7399 | 689 endfunction |
| 6768 | 690 |
| 7017 | 691 |
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692 function res = cf_ub_lb (x, lbidx, ubidx) |
| 5289 | 693 |
| 6768 | 694 ## combine constraint function with ub and lb |
| 695 global __sqp_cifcn__ __sqp_lb__ __sqp_ub__ | |
| 696 | |
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697 if (isempty (__sqp_cifcn__)) |
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698 res = [x(lbidx,1)-__sqp_lb__; __sqp_ub__-x(ubidx,1)]; |
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699 else |
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700 res = [feval(__sqp_cifcn__,x); \ |
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701 x(lbidx,1)-__sqp_lb__; __sqp_ub__-x(ubidx,1)]; |
| 6768 | 702 endif |
| 5289 | 703 |
| 7399 | 704 endfunction |
| 6768 | 705 |
| 7017 | 706 |
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707 function res = cigrad_ub_lb (x, bgrad) |
| 6768 | 708 |
| 709 global __sqp_cif__ | |
| 710 | |
| 711 cigradfcn = @fd_ci_jac; | |
| 712 | |
| 713 if (iscell (__sqp_cif__) && length (__sqp_cif__) > 1) | |
| 714 cigradfcn = __sqp_cif__{2}; | |
| 715 endif | |
|
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716 |
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717 if (isempty (cigradfcn)) |
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718 res = bgrad; |
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719 else |
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720 res = [feval(cigradfcn,x); bgrad]; |
| 6768 | 721 endif |
| 722 | |
| 7399 | 723 endfunction |
| 7361 | 724 |
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725 # Utility function used to debug sqp |
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726 function report (iter, qp_iter, alpha, nfun, obj) |
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727 |
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728 if (nargin == 0) |
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729 printf (" Itn ItQP Step Nfun Objective\n"); |
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730 else |
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731 printf ("%5d %4d %8.1g %5d %13.6e\n", iter, qp_iter, alpha, nfun, obj); |
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732 endif |
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733 |
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734 endfunction |
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735 |
|
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736 |
|
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737 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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738 %% Test Code |
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739 |
|
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740 %!function r = __g (x) |
| 7371 | 741 %! r = [sumsq(x)-10; |
| 742 %! x(2)*x(3)-5*x(4)*x(5); | |
| 743 %! x(1)^3+x(2)^3+1 ]; | |
|
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744 %!endfunction |
| 7361 | 745 %! |
|
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746 %!function obj = __phi (x) |
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747 %! obj = exp (prod (x)) - 0.5*(x(1)^3 + x(2)^3 + 1)^2; |
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748 %!endfunction |
| 7361 | 749 %! |
| 750 %!test | |
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751 %! |
| 7361 | 752 %! x0 = [-1.8; 1.7; 1.9; -0.8; -0.8]; |
| 753 %! | |
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754 %! [x, obj, info, iter, nf, lambda] = sqp (x0, @__phi, @__g, []); |
| 7361 | 755 %! |
| 756 %! x_opt = [-1.717143501952599; | |
| 757 %! 1.595709610928535; | |
| 758 %! 1.827245880097156; | |
| 759 %! -0.763643103133572; | |
| 760 %! -0.763643068453300]; | |
| 761 %! | |
| 7371 | 762 %! obj_opt = 0.0539498477702739; |
| 7361 | 763 %! |
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764 %! assert (x, x_opt, 5*sqrt (eps)); |
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765 %! assert (obj, obj_opt, sqrt (eps)); |
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766 |
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767 %% Test input validation |
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768 %!error sqp () |
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769 %!error sqp (1) |
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770 %!error sqp (1,2,3,4,5,6,7,8,9) |
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771 %!error sqp (1,2,3,4,5) |
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772 %!error sqp (ones (2,2)) |
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773 %!error sqp (1, cell (4,1)) |
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774 %!error sqp (1, cell (3,1), cell (3,1)) |
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775 %!error sqp (1, cell (3,1), cell (2,1), cell (3,1)) |
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776 %!error sqp (1, cell (3,1), cell (2,1), cell (2,1), ones (2,2),[]) |
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777 %!error sqp (1, cell (3,1), cell (2,1), cell (2,1),[], ones (2,2)) |
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778 %!error sqp (1, cell (3,1), cell (2,1), cell (2,1),1,-1) |
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779 %!error sqp (1, cell (3,1), cell (2,1), cell (2,1),[],[], ones (2,2)) |
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780 %!error sqp (1, cell (3,1), cell (2,1), cell (2,1),[],[],-1) |
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781 %!error sqp (1, cell (3,1), cell (2,1), cell (2,1),[],[],1.5) |
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782 %!error sqp (1, cell (3,1), cell (2,1), cell (2,1),[],[],[], ones (2,2)) |
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f3d52523cde1
Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents:
14327
diff
changeset
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783 %!error sqp (1, cell (3,1), cell (2,1), cell (2,1),[],[],[],-1) |