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maint: update copyright notices for 2012
author John W. Eaton <jwe@octave.org>
date Mon, 02 Jan 2012 14:25:41 -0500
parents b9a89ca0fb75
children 4d917a6a858b
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14138
72c96de7a403 maint: update copyright notices for 2012
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1 ## Copyright (C) 2000-2012 Gabriele Pannocchia.
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {[@var{x}, @var{obj}, @var{info}, @var{lambda}] =} qp (@var{x0}, @var{H})
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21 ## @deftypefnx {Function File} {[@var{x}, @var{obj}, @var{info}, @var{lambda}] =} qp (@var{x0}, @var{H}, @var{q})
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22 ## @deftypefnx {Function File} {[@var{x}, @var{obj}, @var{info}, @var{lambda}] =} qp (@var{x0}, @var{H}, @var{q}, @var{A}, @var{b})
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23 ## @deftypefnx {Function File} {[@var{x}, @var{obj}, @var{info}, @var{lambda}] =} qp (@var{x0}, @var{H}, @var{q}, @var{A}, @var{b}, @var{lb}, @var{ub})
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24 ## @deftypefnx {Function File} {[@var{x}, @var{obj}, @var{info}, @var{lambda}] =} qp (@var{x0}, @var{H}, @var{q}, @var{A}, @var{b}, @var{lb}, @var{ub}, @var{A_lb}, @var{A_in}, @var{A_ub})
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25 ## @deftypefnx {Function File} {[@var{x}, @var{obj}, @var{info}, @var{lambda}] =} qp (@dots{}, @var{options})
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26 ## Solve the quadratic program
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27 ## @tex
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28 ## $$
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29 ## \min_x {1 \over 2} x^T H x + x^T q
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30 ## $$
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31 ## @end tex
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32 ## @ifnottex
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33 ##
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34 ## @example
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35 ## @group
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36 ## min 0.5 x'*H*x + x'*q
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37 ## x
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38 ## @end group
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39 ## @end example
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40 ##
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41 ## @end ifnottex
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42 ## subject to
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43 ## @tex
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44 ## $$
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45 ## Ax = b \qquad lb \leq x \leq ub \qquad A_{lb} \leq A_{in} \leq A_{ub}
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46 ## $$
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47 ## @end tex
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48 ## @ifnottex
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49 ##
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50 ## @example
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51 ## @group
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52 ## A*x = b
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53 ## lb <= x <= ub
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54 ## A_lb <= A_in*x <= A_ub
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55 ## @end group
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56 ## @end example
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57 ##
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58 ## @end ifnottex
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59 ## @noindent
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60 ## using a null-space active-set method.
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61 ##
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62 ## Any bound (@var{A}, @var{b}, @var{lb}, @var{ub}, @var{A_lb},
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63 ## @var{A_ub}) may be set to the empty matrix (@code{[]}) if not
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64 ## present. If the initial guess is feasible the algorithm is faster.
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65 ##
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66 ## @table @var
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67 ## @item options
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68 ## An optional structure containing the following
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69 ## parameter(s) used to define the behavior of the solver. Missing elements
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70 ## in the structure take on default values, so you only need to set the
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71 ## elements that you wish to change from the default.
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72 ##
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73 ## @table @code
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74 ## @item MaxIter (default: 200)
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75 ## Maximum number of iterations.
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76 ## @end table
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77 ## @end table
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78 ##
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79 ## @table @var
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80 ## @item info
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81 ## Structure containing run-time information about the algorithm. The
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82 ## following fields are defined:
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83 ##
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84 ## @table @code
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85 ## @item solveiter
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86 ## The number of iterations required to find the solution.
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87 ##
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88 ## @item info
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89 ## An integer indicating the status of the solution.
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90 ##
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91 ## @table @asis
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92 ## @item 0
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93 ## The problem is feasible and convex. Global solution found.
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94 ##
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95 ## @item 1
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96 ## The problem is not convex. Local solution found.
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97 ##
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98 ## @item 2
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99 ## The problem is not convex and unbounded.
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100 ##
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101 ## @item 3
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102 ## Maximum number of iterations reached.
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103 ##
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104 ## @item 6
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105 ## The problem is infeasible.
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106 ## @end table
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107 ## @end table
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108 ## @end table
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109 ## @end deftypefn
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110
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111 ## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup.
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112 ## PKG_ADD: [~] = __all_opts__ ("qp");
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113
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114 function [x, obj, INFO, lambda] = qp (x0, H, varargin)
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115
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116 nargs = nargin;
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117
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118 if (nargin == 1 && ischar (x0) && strcmp (x0, 'defaults'))
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119 x = optimset ("MaxIter", 200);
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120 return;
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121 endif
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122
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123 if (nargs > 2 && isstruct (varargin{end}))
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124 options = varargin{end};
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125 nargs--;
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126 else
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127 options = struct ();
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128 endif
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129
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130 if (nargs >= 3)
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131 q = varargin{1};
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132 else
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133 q = [];
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134 endif
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135
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136 if (nargs >= 5)
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diff changeset
137 A = varargin{2};
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diff changeset
138 b = varargin{3};
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diff changeset
139 else
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140 A = [];
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diff changeset
141 b = [];
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diff changeset
142 endif
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parents: 9872
diff changeset
143
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diff changeset
144 if (nargs >= 7)
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diff changeset
145 lb = varargin{4};
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diff changeset
146 ub = varargin{5};
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diff changeset
147 else
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148 lb = [];
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149 ub = [];
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150 endif
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diff changeset
151
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diff changeset
152 if (nargs == 10)
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diff changeset
153 A_lb = varargin{6};
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154 A_in = varargin{7};
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diff changeset
155 A_ub = varargin{8};
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156 else
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157 A_lb = [];
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158 A_in = [];
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diff changeset
159 A_ub = [];
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160 endif
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161
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diff changeset
162 if (nargs == 2 || nargs == 3 || nargs == 5 || nargs == 7 || nargs == 10)
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diff changeset
163
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17ce2a700a97 qp.m: Add missing semicolon.
Ben Abbott <bpabbott@mac.com>
parents: 10060
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164 maxit = optimget (options, "MaxIter", 200);
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165
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166 ## Checking the quadratic penalty
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167 if (! issquare (H))
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168 error ("qp: quadratic penalty matrix not square");
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169 elseif (! ishermitian (H))
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170 ## warning ("qp: quadratic penalty matrix not hermitian");
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171 H = (H + H')/2;
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172 endif
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173 n = rows (H);
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174
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175 ## Checking the initial guess (if empty it is resized to the
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176 ## right dimension and filled with 0)
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177 if (isempty (x0))
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178 x0 = zeros (n, 1);
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179 elseif (numel (x0) != n)
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180 error ("qp: the initial guess has incorrect length");
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181 endif
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182
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183 ## Linear penalty.
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184 if (isempty (q))
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185 q = zeros (n, 1);
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186 elseif (numel (q) != n)
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187 error ("qp: the linear term has incorrect length");
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188 endif
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189
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190 ## Equality constraint matrices
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191 if (isempty (A) || isempty (b))
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192 A = zeros (0, n);
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193 b = zeros (0, 1);
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194 n_eq = 0;
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195 else
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196 [n_eq, n1] = size (A);
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197 if (n1 != n)
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198 error ("qp: equality constraint matrix has incorrect column dimension");
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199 endif
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200 if (numel (b) != n_eq)
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201 error ("qp: equality constraint matrix and vector have inconsistent dimension");
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202 endif
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203 endif
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204
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205 ## Bound constraints
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206 Ain = zeros (0, n);
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207 bin = zeros (0, 1);
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208 n_in = 0;
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209 if (nargs > 5)
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210 if (! isempty (lb))
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211 if (numel (lb) != n)
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212 error ("qp: lower bound has incorrect length");
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213 elseif (isempty (ub))
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214 Ain = [Ain; eye(n)];
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215 bin = [bin; lb];
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216 endif
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217 endif
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218
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219 if (! isempty (ub))
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220 if (numel (ub) != n)
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221 error ("qp: upper bound has incorrect length");
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222 elseif (isempty (lb))
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223 Ain = [Ain; -eye(n)];
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224 bin = [bin; -ub];
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225 endif
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226 endif
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227
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228 if (! isempty (lb) && ! isempty (ub))
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229 rtol = sqrt (eps);
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230 for i = 1:n
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231 if (abs(lb (i) - ub(i)) < rtol*(1 + max (abs (lb(i) + ub(i)))))
8280
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232 ## These are actually an equality constraint
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233 tmprow = zeros(1,n);
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234 tmprow(i) = 1;
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235 A = [A;tmprow];
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236 b = [b; 0.5*(lb(i) + ub(i))];
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237 n_eq = n_eq + 1;
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238 else
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239 tmprow = zeros(1,n);
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240 tmprow(i) = 1;
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241 Ain = [Ain; tmprow; -tmprow];
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242 bin = [bin; lb(i); -ub(i)];
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243 n_in = n_in + 2;
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244 endif
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245 endfor
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246 endif
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247 endif
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248
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249 ## Inequality constraints
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250 if (nargs > 7)
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251 [dimA_in, n1] = size (A_in);
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252 if (n1 != n)
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253 error ("qp: inequality constraint matrix has incorrect column dimension");
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254 else
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255 if (! isempty (A_lb))
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256 if (numel (A_lb) != dimA_in)
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257 error ("qp: inequality constraint matrix and lower bound vector inconsistent");
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258 elseif (isempty (A_ub))
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259 Ain = [Ain; A_in];
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260 bin = [bin; A_lb];
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261 endif
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262 endif
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263 if (! isempty (A_ub))
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264 if (numel (A_ub) != dimA_in)
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265 error ("qp: inequality constraint matrix and upper bound vector inconsistent");
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266 elseif (isempty (A_lb))
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267 Ain = [Ain; -A_in];
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268 bin = [bin; -A_ub];
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269 endif
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270 endif
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271
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272 if (! isempty (A_lb) && ! isempty (A_ub))
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273 rtol = sqrt (eps);
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274 for i = 1:dimA_in
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275 if (abs (A_lb(i) - A_ub(i)) < rtol*(1 + max (abs (A_lb(i) + A_ub(i)))))
8280
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276 ## These are actually an equality constraint
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parents: 10540
diff changeset
277 tmprow = A_in(i,:);
8280
5ee11a81688e qp.m: convert b <= x <= b and b <= A*x <= b to equality constraints
Gabriele Pannocchia <g.pannocchia@ing.unipi.it>
parents: 7795
diff changeset
278 A = [A;tmprow];
5ee11a81688e qp.m: convert b <= x <= b and b <= A*x <= b to equality constraints
Gabriele Pannocchia <g.pannocchia@ing.unipi.it>
parents: 7795
diff changeset
279 b = [b; 0.5*(A_lb(i) + A_ub(i))];
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
280 n_eq = n_eq + 1;
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
281 else
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
282 tmprow = A_in(i,:);
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
283 Ain = [Ain; tmprow; -tmprow];
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
284 bin = [bin; A_lb(i); -A_ub(i)];
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
285 n_in = n_in + 2;
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
286 endif
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
287 endfor
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
288 endif
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
289 endif
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
290 endif
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
291
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
292 ## Now we should have the following QP:
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
293 ##
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
294 ## min_x 0.5*x'*H*x + x'*q
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
295 ## s.t. A*x = b
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
296 ## Ain*x >= bin
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
297
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
298 ## Discard inequality constraints that have -Inf bounds since those
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
299 ## will never be active.
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
300 idx = isinf (bin) & bin < 0;
6523
589c8dbba916 [project @ 2007-04-12 19:06:44 by jwe]
jwe
parents: 6417
diff changeset
301
6526
2a715c6409a5 [project @ 2007-04-13 20:31:50 by jwe]
jwe
parents: 6523
diff changeset
302 bin(idx) = [];
2a715c6409a5 [project @ 2007-04-13 20:31:50 by jwe]
jwe
parents: 6523
diff changeset
303 Ain(idx,:) = [];
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
304
10059
665ad34efeed qp.m: handle optimset options
Joshua Redstone <redstone@gmail.com>, John W. Eaton <jwe@octave.org>
parents: 9872
diff changeset
305 n_in = numel (bin);
5310
2fbcdc356fc7 [project @ 2005-04-27 15:38:53 by jwe]
jwe
parents: 5307
diff changeset
306
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
307 ## Check if the initial guess is feasible.
7795
df9519e9990c Handle single precision eps values
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
308 if (isa (x0, "single") || isa (H, "single") || isa (q, "single") || isa (A, "single")
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
309 || isa (b, "single"))
7795
df9519e9990c Handle single precision eps values
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
310 rtol = sqrt (eps ("single"));
df9519e9990c Handle single precision eps values
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
311 else
df9519e9990c Handle single precision eps values
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
312 rtol = sqrt (eps);
df9519e9990c Handle single precision eps values
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
313 endif
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
314
8280
5ee11a81688e qp.m: convert b <= x <= b and b <= A*x <= b to equality constraints
Gabriele Pannocchia <g.pannocchia@ing.unipi.it>
parents: 7795
diff changeset
315 eq_infeasible = (n_eq > 0 && norm (A*x0-b) > rtol*(1+abs (b)));
5ee11a81688e qp.m: convert b <= x <= b and b <= A*x <= b to equality constraints
Gabriele Pannocchia <g.pannocchia@ing.unipi.it>
parents: 7795
diff changeset
316 in_infeasible = (n_in > 0 && any (Ain*x0-bin < -rtol*(1+abs (bin))));
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
317
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
318 info = 0;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
319 if (eq_infeasible || in_infeasible)
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
320 ## The initial guess is not feasible.
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
321 ## First define xbar that is feasible with respect to the equality
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
322 ## constraints.
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
323 if (eq_infeasible)
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
324 if (rank (A) < n_eq)
11589
b0084095098e missing semicolons in script files
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
325 error ("qp: equality constraint matrix must be full row rank");
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
326 endif
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
327 xbar = pinv (A) * b;
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
328 else
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
329 xbar = x0;
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
330 endif
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
331
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
332 ## Check if xbar is feasible with respect to the inequality
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
333 ## constraints also.
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
334 if (n_in > 0)
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
335 res = Ain * xbar - bin;
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
336 if (any (res < -rtol * (1 + abs (bin))))
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
337 ## xbar is not feasible with respect to the inequality
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
338 ## constraints. Compute a step in the null space of the
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
339 ## equality constraints, by solving a QP. If the slack is
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
340 ## small, we have a feasible initial guess. Otherwise, the
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
341 ## problem is infeasible.
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
342 if (n_eq > 0)
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
343 Z = null (A);
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
344 if (isempty (Z))
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
345 ## The problem is infeasible because A is square and full
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
346 ## rank, but xbar is not feasible.
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
347 info = 6;
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
348 endif
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
349 endif
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
350
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
351 if (info != 6)
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
352 ## Solve an LP with additional slack variables to find
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
353 ## a feasible starting point.
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
354 gamma = eye (n_in);
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
355 if (n_eq > 0)
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
356 Atmp = [Ain*Z, gamma];
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
357 btmp = -res;
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
358 else
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
359 Atmp = [Ain, gamma];
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
360 btmp = bin;
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
361 endif
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
362 ctmp = [zeros(n-n_eq, 1); ones(n_in, 1)];
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
363 lb = [-Inf(n-n_eq,1); zeros(n_in,1)];
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
364 ub = [];
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
365 ctype = repmat ("L", n_in, 1);
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
366 [P, dummy, status] = glpk (ctmp, Atmp, btmp, lb, ub, ctype);
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
367 if ((status == 180 || status == 181 || status == 151)
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
368 && all (abs (P(n-n_eq+1:end)) < rtol * (1 + norm (btmp))))
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
369 ## We found a feasible starting point
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
370 if (n_eq > 0)
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
371 x0 = xbar + Z*P(1:n-n_eq);
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
372 else
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
373 x0 = P(1:n);
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
374 endif
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
375 else
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
376 ## The problem is infeasible
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
377 info = 6;
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
378 endif
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
379 endif
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
380 else
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
381 ## xbar is feasible. We use it a starting point.
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
382 x0 = xbar;
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
383 endif
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
384 else
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
385 ## xbar is feasible. We use it a starting point.
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
386 x0 = xbar;
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
387 endif
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
388 endif
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
389
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
390 if (info == 0)
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
391 ## The initial (or computed) guess is feasible.
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
392 ## We call the solver.
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
393 [x, lambda, info, iter] = __qp__ (x0, H, q, A, b, Ain, bin, maxit);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
394 else
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
395 iter = 0;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
396 x = x0;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
397 lambda = [];
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
398 endif
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
399 obj = 0.5 * x' * H * x + q' * x;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
400 INFO.solveiter = iter;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
401 INFO.info = info;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
402
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
403 else
6046
34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe]
jwe
parents: 5310
diff changeset
404 print_usage ();
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
405 endif
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
406
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
407 endfunction