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update Octave Project Developers copyright for the new year In files that have the "Octave Project Developers" copyright notice, update for 2020.
author John W. Eaton <jwe@octave.org>
date Mon, 06 Jan 2020 22:29:51 -0500
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27919
1891570abac8 update Octave Project Developers copyright for the new year
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1 ## Copyright (C) 2005-2020 The Octave Project Developers
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2 ##
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3 ## See the file COPYRIGHT.md in the top-level directory of this distribution
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4 ## or <https://octave.org/COPYRIGHT.html/>.
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5 ##
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6 ##
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7 ## This file is part of Octave.
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8 ##
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9 ## Octave is free software: you can redistribute it and/or modify it
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10 ## under the terms of the GNU General Public License as published by
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11 ## the Free Software Foundation, either version 3 of the License, or
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12 ## (at your option) any later version.
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13 ##
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14 ## Octave is distributed in the hope that it will be useful, but
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15 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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16 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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17 ## GNU General Public License for more details.
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18 ##
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19 ## You should have received a copy of the GNU General Public License
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20 ## along with Octave; see the file COPYING. If not, see
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21 ## <https://www.gnu.org/licenses/>.
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22
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23 ## -*- texinfo -*-
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24 ## @deftypefn {} {[@var{x}, @var{obj}, @var{info}, @var{iter}, @var{nf}, @var{lambda}] =} sqp (@var{x0}, @var{phi})
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25 ## @deftypefnx {} {[@dots{}] =} sqp (@var{x0}, @var{phi}, @var{g})
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26 ## @deftypefnx {} {[@dots{}] =} sqp (@var{x0}, @var{phi}, @var{g}, @var{h})
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27 ## @deftypefnx {} {[@dots{}] =} sqp (@var{x0}, @var{phi}, @var{g}, @var{h}, @var{lb}, @var{ub})
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28 ## @deftypefnx {} {[@dots{}] =} sqp (@var{x0}, @var{phi}, @var{g}, @var{h}, @var{lb}, @var{ub}, @var{maxiter})
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29 ## @deftypefnx {} {[@dots{}] =} sqp (@var{x0}, @var{phi}, @var{g}, @var{h}, @var{lb}, @var{ub}, @var{maxiter}, @var{tol})
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30 ## Minimize an objective function using sequential quadratic programming (SQP).
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31 ##
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32 ## Solve the nonlinear program
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33 ## @tex
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34 ## $$
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35 ## \min_x \phi (x)
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36 ## $$
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37 ## @end tex
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38 ## @ifnottex
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39 ##
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40 ## @example
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41 ## @group
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42 ## min phi (x)
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43 ## x
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44 ## @end group
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45 ## @end example
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46 ##
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47 ## @end ifnottex
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48 ## subject to
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49 ## @tex
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50 ## $$
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51 ## g(x) = 0 \qquad h(x) \geq 0 \qquad lb \leq x \leq ub
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52 ## $$
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53 ## @end tex
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54 ## @ifnottex
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55 ##
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56 ## @example
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57 ## @group
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58 ## g(x) = 0
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59 ## h(x) >= 0
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60 ## lb <= x <= ub
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61 ## @end group
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62 ## @end example
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63 ##
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64 ## @end ifnottex
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65 ## @noindent
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66 ## using a sequential quadratic programming method.
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67 ##
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68 ## The first argument is the initial guess for the vector @var{x0}.
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69 ##
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70 ## The second argument is a function handle pointing to the objective function
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71 ## @var{phi}. The objective function must accept one vector argument and
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72 ## return a scalar.
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73 ##
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74 ## The second argument may also be a 2- or 3-element cell array of function
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75 ## handles. The first element should point to the objective function, the
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76 ## second should point to a function that computes the gradient of the
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77 ## objective function, and the third should point to a function that computes
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78 ## the Hessian of the objective function. If the gradient function is not
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79 ## supplied, the gradient is computed by finite differences. If the Hessian
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80 ## function is not supplied, a BFGS update formula is used to approximate the
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81 ## Hessian.
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82 ##
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83 ## When supplied, the gradient function @code{@var{phi}@{2@}} must accept one
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84 ## vector argument and return a vector. When supplied, the Hessian function
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85 ## @code{@var{phi}@{3@}} must accept one vector argument and return a matrix.
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86 ##
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87 ## The third and fourth arguments @var{g} and @var{h} are function handles
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88 ## pointing to functions that compute the equality constraints and the
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89 ## inequality constraints, respectively. If the problem does not have
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90 ## equality (or inequality) constraints, then use an empty matrix ([]) for
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91 ## @var{g} (or @var{h}). When supplied, these equality and inequality
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92 ## constraint functions must accept one vector argument and return a vector.
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93 ##
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94 ## The third and fourth arguments may also be 2-element cell arrays of
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95 ## function handles. The first element should point to the constraint
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96 ## function and the second should point to a function that computes the
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97 ## gradient of the constraint function:
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98 ## @tex
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99 ## $$
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100 ## \Bigg( {\partial f(x) \over \partial x_1},
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101 ## {\partial f(x) \over \partial x_2}, \ldots,
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102 ## {\partial f(x) \over \partial x_N} \Bigg)^T
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103 ## $$
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104 ## @end tex
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105 ## @ifnottex
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106 ##
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107 ## @example
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108 ## @group
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109 ## [ d f(x) d f(x) d f(x) ]
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110 ## transpose ( [ ------ ----- ... ------ ] )
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111 ## [ dx_1 dx_2 dx_N ]
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112 ## @end group
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113 ## @end example
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114 ##
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115 ## @end ifnottex
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116 ## The fifth and sixth arguments, @var{lb} and @var{ub}, contain lower and
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117 ## upper bounds on @var{x}. These must be consistent with the equality and
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118 ## inequality constraints @var{g} and @var{h}. If the arguments are vectors
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119 ## then @var{x}(i) is bound by @var{lb}(i) and @var{ub}(i). A bound can also
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120 ## be a scalar in which case all elements of @var{x} will share the same
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121 ## bound. If only one bound (lb, ub) is specified then the other will
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122 ## default to (-@var{realmax}, +@var{realmax}).
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123 ##
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124 ## The seventh argument @var{maxiter} specifies the maximum number of
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125 ## iterations. The default value is 100.
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126 ##
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127 ## The eighth argument @var{tol} specifies the tolerance for the stopping
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128 ## criteria. The default value is @code{sqrt (eps)}.
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129 ##
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130 ## The value returned in @var{info} may be one of the following:
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131 ##
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132 ## @table @asis
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133 ## @item 101
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134 ## The algorithm terminated normally.
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135 ## All constraints meet the specified tolerance.
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136 ##
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137 ## @item 102
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138 ## The BFGS update failed.
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139 ##
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140 ## @item 103
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141 ## The maximum number of iterations was reached.
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142 ##
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143 ## @item 104
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144 ## The stepsize has become too small, i.e.,
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145 ## @tex
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146 ## $\Delta x,$
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147 ## @end tex
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148 ## @ifnottex
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149 ## delta @var{x},
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150 ## @end ifnottex
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151 ## is less than @code{@var{tol} * norm (x)}.
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152 ## @end table
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153 ##
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154 ## An example of calling @code{sqp}:
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155 ##
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156 ## @example
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157 ## function r = g (x)
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158 ## r = [ sumsq(x)-10;
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159 ## x(2)*x(3)-5*x(4)*x(5);
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160 ## x(1)^3+x(2)^3+1 ];
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161 ## endfunction
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162 ##
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163 ## function obj = phi (x)
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164 ## obj = exp (prod (x)) - 0.5*(x(1)^3+x(2)^3+1)^2;
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165 ## endfunction
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166 ##
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167 ## x0 = [-1.8; 1.7; 1.9; -0.8; -0.8];
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168 ##
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169 ## [x, obj, info, iter, nf, lambda] = sqp (x0, @@phi, @@g, [])
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170 ##
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171 ## x =
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172 ##
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173 ## -1.71714
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174 ## 1.59571
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175 ## 1.82725
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176 ## -0.76364
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177 ## -0.76364
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178 ##
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179 ## obj = 0.053950
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180 ## info = 101
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181 ## iter = 8
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182 ## nf = 10
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183 ## lambda =
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184 ##
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185 ## -0.0401627
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186 ## 0.0379578
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187 ## -0.0052227
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188 ## @end example
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189 ##
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190 ## @seealso{qp}
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191 ## @end deftypefn
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192
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193 function [x, obj, info, iter, nf, lambda] = sqp (x0, objf, cef, cif, lb, ub, maxiter, tolerance)
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194
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195 globals = struct (); # data and handles, needed and changed by subfunctions
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196
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197 if (nargin < 2 || nargin > 8 || nargin == 5)
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198 print_usage ();
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199 endif
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200
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201 if (! isvector (x0))
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202 error ("sqp: X0 must be a vector");
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203 endif
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204 if (rows (x0) == 1)
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205 x0 = x0';
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206 endif
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207
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208 have_grd = 0;
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209 have_hess = 0;
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210 if (iscell (objf))
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211 switch (numel (objf))
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212 case 1
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213 obj_fun = objf{1};
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214 obj_grd = @(x, obj) fd_obj_grd (x, obj, obj_fun);
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215 case 2
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216 obj_fun = objf{1};
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217 obj_grd = objf{2};
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218 have_grd = 1;
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219 case 3
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220 obj_fun = objf{1};
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221 obj_grd = objf{2};
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222 obj_hess = objf{3};
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223 have_grd = 1;
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224 have_hess = 1;
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225 otherwise
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226 error ("sqp: invalid objective function specification");
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227 endswitch
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228 else
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229 obj_fun = objf; # No cell array, only obj_fun set
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230 obj_grd = @(x, obj) fd_obj_grd (x, obj, obj_fun);
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231 endif
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232
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233 ce_fun = @empty_cf;
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234 ce_grd = @empty_jac;
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235 if (nargin > 2)
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236 if (iscell (cef))
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237 switch (numel (cef))
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238 case 1
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239 ce_fun = cef{1};
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240 ce_grd = @(x) fd_ce_jac (x, ce_fun);
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241 case 2
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242 ce_fun = cef{1};
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243 ce_grd = cef{2};
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244 otherwise
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245 error ("sqp: invalid equality constraint function specification");
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246 endswitch
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247 elseif (! isempty (cef))
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248 ce_fun = cef; # No cell array, only constraint equality function set
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249 ce_grd = @(x) fd_ce_jac (x, ce_fun);
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250 endif
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251 endif
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252
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253 ci_fun = @empty_cf;
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254 ci_grd = @empty_jac;
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255 if (nargin > 3)
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256 ## constraint function given by user with possible gradient
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257 globals.cif = cif;
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258 ## constraint function given by user without gradient
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259 globals.cifcn = @empty_cf;
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260 if (iscell (cif))
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261 if (length (cif) > 0)
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262 globals.cifcn = cif{1};
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263 endif
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264 elseif (! isempty (cif))
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265 globals.cifcn = cif;
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266 endif
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267
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268 if (nargin < 5 || (nargin > 5 && isempty (lb) && isempty (ub)))
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269 ## constraint inequality function only without any bounds
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270 ci_grd = @(x) fd_ci_jac (x, globals.cifcn);
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271 if (iscell (cif))
16933
e39f00a32dc7 maint: Use parentheses around condition for switch(),while(),if() statements.
Rik <rik@octave.org>
parents: 16064
diff changeset
272 switch (length (cif))
17174
c3c1ebfaa7dc maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents: 16933
diff changeset
273 case 1
c3c1ebfaa7dc maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents: 16933
diff changeset
274 ci_fun = cif{1};
c3c1ebfaa7dc maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents: 16933
diff changeset
275 case 2
c3c1ebfaa7dc maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents: 16933
diff changeset
276 ci_fun = cif{1};
c3c1ebfaa7dc maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents: 16933
diff changeset
277 ci_grd = cif{2};
c3c1ebfaa7dc maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents: 16933
diff changeset
278 otherwise
c3c1ebfaa7dc maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents: 16933
diff changeset
279 error ("sqp: invalid inequality constraint function specification");
10678
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Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
280 endswitch
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
281 elseif (! isempty (cif))
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
282 ci_fun = cif; # No cell array, only constraint inequality function set
5289
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jwe
parents:
diff changeset
283 endif
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
284 else
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
285 ## constraint inequality function with bounds present
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
286 lb_idx = ub_idx = true (size (x0));
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
287 ub_grad = - (lb_grad = eye (rows (x0)));
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
288 if (isvector (lb))
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
289 globals.lb = tmp_lb = lb(:);
11347
2726132f77f6 sqp.m: Remove never violated Inf bounds from computation (bug #31742)
Rik <octave@nomad.inbox5.com>
parents: 11290
diff changeset
290 lb_idx(:) = tmp_idx = (lb != -Inf);
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
291 globals.lb = globals.lb(tmp_idx, 1);
11347
2726132f77f6 sqp.m: Remove never violated Inf bounds from computation (bug #31742)
Rik <octave@nomad.inbox5.com>
parents: 11290
diff changeset
292 lb_grad = lb_grad(lb_idx, :);
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
293 elseif (isempty (lb))
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
294 if (isa (x0, "single"))
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
295 globals.lb = tmp_lb = -realmax ("single");
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
296 else
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
297 globals.lb = tmp_lb = -realmax;
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10542
diff changeset
298 endif
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
299 else
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
300 error ("sqp: invalid lower bound");
6768
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jwe
parents: 6741
diff changeset
301 endif
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
302
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
303 if (isvector (ub))
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
304 globals.ub = tmp_ub = ub(:);
11347
2726132f77f6 sqp.m: Remove never violated Inf bounds from computation (bug #31742)
Rik <octave@nomad.inbox5.com>
parents: 11290
diff changeset
305 ub_idx(:) = tmp_idx = (ub != Inf);
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
306 globals.ub = globals.ub(tmp_idx, 1);
11347
2726132f77f6 sqp.m: Remove never violated Inf bounds from computation (bug #31742)
Rik <octave@nomad.inbox5.com>
parents: 11290
diff changeset
307 ub_grad = ub_grad(ub_idx, :);
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
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parents: 10549
diff changeset
308 elseif (isempty (ub))
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
309 if (isa (x0, "single"))
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
310 globals.ub = tmp_ub = realmax ("single");
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
311 else
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
312 globals.ub = tmp_ub = realmax;
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10542
diff changeset
313 endif
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
314 else
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
315 error ("sqp: invalid upper bound");
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
316 endif
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
317
11347
2726132f77f6 sqp.m: Remove never violated Inf bounds from computation (bug #31742)
Rik <octave@nomad.inbox5.com>
parents: 11290
diff changeset
318 if (any (tmp_lb > tmp_ub))
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
319 error ("sqp: upper bound smaller than lower bound");
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
320 endif
11347
2726132f77f6 sqp.m: Remove never violated Inf bounds from computation (bug #31742)
Rik <octave@nomad.inbox5.com>
parents: 11290
diff changeset
321 bounds_grad = [lb_grad; ub_grad];
19833
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 19697
diff changeset
322 ci_fun = @(x) cf_ub_lb (x, lb_idx, ub_idx, globals);
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 19697
diff changeset
323 ci_grd = @(x) cigrad_ub_lb (x, bounds_grad, globals);
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
324 endif
5289
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jwe
parents:
diff changeset
325
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
326 endif # if (nargin > 3)
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
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parents: 10549
diff changeset
327
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
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parents: 10549
diff changeset
328 iter_max = 100;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
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parents: 10549
diff changeset
329 if (nargin > 6 && ! isempty (maxiter))
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
330 if (isscalar (maxiter) && maxiter > 0 && fix (maxiter) == maxiter)
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
331 iter_max = maxiter;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
332 else
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
333 error ("sqp: invalid number of maximum iterations");
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
334 endif
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
335 endif
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
336
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
337 tol = sqrt (eps);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
338 if (nargin > 7 && ! isempty (tolerance))
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
339 if (isscalar (tolerance) && tolerance > 0)
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
340 tol = tolerance;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
341 else
11472
1740012184f9 Use uppercase for variable names in error() strings to match Info documentation. Only m-files done.
Rik <octave@nomad.inbox5.com>
parents: 11371
diff changeset
342 error ("sqp: invalid value for TOLERANCE");
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
343 endif
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
344 endif
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
345
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
346 ## Initialize variables for search loop
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
347 ## Seed x with initial guess and evaluate objective function, constraints,
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
348 ## and gradients at initial value x0.
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
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parents: 10549
diff changeset
349 ##
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
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parents: 10549
diff changeset
350 ## obj_fun -- objective function
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
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parents: 10549
diff changeset
351 ## obj_grad -- objective gradient
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
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parents: 10549
diff changeset
352 ## ce_fun -- equality constraint functions
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
353 ## ci_fun -- inequality constraint functions
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
354 ## A == [grad_{x_1} cx_fun, grad_{x_2} cx_fun, ..., grad_{x_n} cx_fun]^T
11587
c792872f8942 all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
355 x = x0;
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
356
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
357 obj = feval (obj_fun, x0);
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
358 globals.nfun = 1;
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
359
26237
34cc6edf2041 sqp.m: Eliminate redundant objective function calls (patch #8073).
Ken Marek <gm.kmarek@gmail.com>
parents: 25054
diff changeset
360 if (have_grd)
34cc6edf2041 sqp.m: Eliminate redundant objective function calls (patch #8073).
Ken Marek <gm.kmarek@gmail.com>
parents: 25054
diff changeset
361 c = feval (obj_grd, x0);
34cc6edf2041 sqp.m: Eliminate redundant objective function calls (patch #8073).
Ken Marek <gm.kmarek@gmail.com>
parents: 25054
diff changeset
362 else
34cc6edf2041 sqp.m: Eliminate redundant objective function calls (patch #8073).
Ken Marek <gm.kmarek@gmail.com>
parents: 25054
diff changeset
363 c = feval (obj_grd, x0, obj);
34cc6edf2041 sqp.m: Eliminate redundant objective function calls (patch #8073).
Ken Marek <gm.kmarek@gmail.com>
parents: 25054
diff changeset
364 endif
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
365
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
366 ## Choose an initial NxN symmetric positive definite Hessian approximation B.
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
367 n = length (x0);
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
368 if (have_hess)
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
369 B = feval (obj_hess, x0);
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
370 else
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
371 B = eye (n, n);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
372 endif
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
373
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
374 ce = feval (ce_fun, x0);
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
375 F = feval (ce_grd, x0);
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
376
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
377 ci = feval (ci_fun, x0);
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
378 C = feval (ci_grd, x0);
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
379
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
380 A = [F; C];
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
381
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
382 ## Choose an initial lambda (x is provided by the caller).
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
383 lambda = 100 * ones (rows (A), 1);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
384
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
385 qp_iter = 1;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
386 alpha = 1;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
387
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
388 info = 0;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
389 iter = 0;
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
390 # report (); # Called with no arguments to initialize reporting
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
391 # report (iter, qp_iter, alpha, __sqp_nfun__, obj);
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
392
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
393 while (++iter < iter_max)
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
394
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
395 ## Check convergence. This is just a simple check on the first
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
396 ## order necessary conditions.
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
397 nr_f = rows (F);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
398
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
399 lambda_e = lambda((1:nr_f)');
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
400 lambda_i = lambda((nr_f+1:end)');
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
401
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
402 con = [ce; ci];
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
403
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
404 t0 = norm (c - A' * lambda);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
405 t1 = norm (ce);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
406 t2 = all (ci >= 0);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
407 t3 = all (lambda_i >= 0);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
408 t4 = norm (lambda .* con);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
409
18255
f58a6cd3f909 sqp.m: Fix return values in sqp (bug #32008).
Arun Giridhar <arungiridhar@gmail.com>
parents: 17744
diff changeset
410 ## Normal convergence. All constraints are satisfied
f58a6cd3f909 sqp.m: Fix return values in sqp (bug #32008).
Arun Giridhar <arungiridhar@gmail.com>
parents: 17744
diff changeset
411 ## and objective has converged.
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
412 if (t2 && t3 && max ([t0; t1; t4]) < tol)
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
413 info = 101;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
414 break;
6382
f74e71ef6612 [project @ 2007-03-05 21:29:40 by jwe]
jwe
parents: 6046
diff changeset
415 endif
f74e71ef6612 [project @ 2007-03-05 21:29:40 by jwe]
jwe
parents: 6046
diff changeset
416
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
417 ## Compute search direction p by solving QP.
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
418 g = -ce;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
419 d = -ci;
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
420
22224
20e0c0b8820c Allow sequential quadratic programs with infeasible QPs (bug #36015).
Lachlan Andrew <lachlanbis@gmail.com>
parents: 21758
diff changeset
421 old_lambda = lambda;
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
422 [p, obj_qp, INFO, lambda] = qp (x, B, c, F, g, [], [], d, C,
26332
d4211810202a qp and sqp: Non-fixed tolerance for qp (bug #53506).
Maor Shutman <maorus12@gmail.com>
parents: 26237
diff changeset
423 Inf (size (d)), struct ("TolX", tol));
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
424
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
425 info = INFO.info;
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
426
18255
f58a6cd3f909 sqp.m: Fix return values in sqp (bug #32008).
Arun Giridhar <arungiridhar@gmail.com>
parents: 17744
diff changeset
427 ## FIXME: check QP solution and attempt to recover if it has failed.
f58a6cd3f909 sqp.m: Fix return values in sqp (bug #32008).
Arun Giridhar <arungiridhar@gmail.com>
parents: 17744
diff changeset
428 ## For now, just warn about possible problems.
19593
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 17744
diff changeset
429
13206
658aa9fd8665 sqp: provide warnings for QP subproblem failures
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
430 id = "Octave:SQP-QP-subproblem";
658aa9fd8665 sqp: provide warnings for QP subproblem failures
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
431 switch (info)
658aa9fd8665 sqp: provide warnings for QP subproblem failures
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
432 case 2
658aa9fd8665 sqp: provide warnings for QP subproblem failures
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
433 warning (id, "sqp: QP subproblem is non-convex and unbounded");
658aa9fd8665 sqp: provide warnings for QP subproblem failures
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
434 case 3
658aa9fd8665 sqp: provide warnings for QP subproblem failures
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
435 warning (id, "sqp: QP subproblem failed to converge in %d iterations",
658aa9fd8665 sqp: provide warnings for QP subproblem failures
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
436 INFO.solveiter);
658aa9fd8665 sqp: provide warnings for QP subproblem failures
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
437 case 6
658aa9fd8665 sqp: provide warnings for QP subproblem failures
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
438 warning (id, "sqp: QP subproblem is infeasible");
22224
20e0c0b8820c Allow sequential quadratic programs with infeasible QPs (bug #36015).
Lachlan Andrew <lachlanbis@gmail.com>
parents: 21758
diff changeset
439 lambda = old_lambda; # The return value was size 0x0 in this case.
13206
658aa9fd8665 sqp: provide warnings for QP subproblem failures
John W. Eaton <jwe@octave.org>
parents: 11587
diff changeset
440 endswitch
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
441
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
442 ## Choose mu such that p is a descent direction for the chosen
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
443 ## merit function phi.
17245
7babcdb9bc13 Use ... instead of \ for line continuation marker.
Stefan Mahr <dac922@gmx.de>
parents: 17174
diff changeset
444 [x_new, alpha, obj_new, globals] = ...
7babcdb9bc13 Use ... instead of \ for line continuation marker.
Stefan Mahr <dac922@gmx.de>
parents: 17174
diff changeset
445 linesearch_L1 (x, p, obj_fun, obj_grd, ce_fun, ci_fun, lambda, ...
26237
34cc6edf2041 sqp.m: Eliminate redundant objective function calls (patch #8073).
Ken Marek <gm.kmarek@gmail.com>
parents: 25054
diff changeset
446 obj, c, globals);
26617
98afb8bbd1f6 maint: Strip trailing whitespace from source files.
John W. Eaton <jwe@octave.org>
parents: 26376
diff changeset
447
26237
34cc6edf2041 sqp.m: Eliminate redundant objective function calls (patch #8073).
Ken Marek <gm.kmarek@gmail.com>
parents: 25054
diff changeset
448 delx = x_new - x;
34cc6edf2041 sqp.m: Eliminate redundant objective function calls (patch #8073).
Ken Marek <gm.kmarek@gmail.com>
parents: 25054
diff changeset
449
34cc6edf2041 sqp.m: Eliminate redundant objective function calls (patch #8073).
Ken Marek <gm.kmarek@gmail.com>
parents: 25054
diff changeset
450 ## Check if step size has become too small (indicates lack of progress).
34cc6edf2041 sqp.m: Eliminate redundant objective function calls (patch #8073).
Ken Marek <gm.kmarek@gmail.com>
parents: 25054
diff changeset
451 if (norm (delx) < tol * norm (x))
34cc6edf2041 sqp.m: Eliminate redundant objective function calls (patch #8073).
Ken Marek <gm.kmarek@gmail.com>
parents: 25054
diff changeset
452 info = 104;
34cc6edf2041 sqp.m: Eliminate redundant objective function calls (patch #8073).
Ken Marek <gm.kmarek@gmail.com>
parents: 25054
diff changeset
453 break;
34cc6edf2041 sqp.m: Eliminate redundant objective function calls (patch #8073).
Ken Marek <gm.kmarek@gmail.com>
parents: 25054
diff changeset
454 endif
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
455
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
456 ## Evaluate objective function, constraints, and gradients at x_new.
26237
34cc6edf2041 sqp.m: Eliminate redundant objective function calls (patch #8073).
Ken Marek <gm.kmarek@gmail.com>
parents: 25054
diff changeset
457 if (have_grd)
34cc6edf2041 sqp.m: Eliminate redundant objective function calls (patch #8073).
Ken Marek <gm.kmarek@gmail.com>
parents: 25054
diff changeset
458 c_new = feval (obj_grd, x_new);
34cc6edf2041 sqp.m: Eliminate redundant objective function calls (patch #8073).
Ken Marek <gm.kmarek@gmail.com>
parents: 25054
diff changeset
459 else
34cc6edf2041 sqp.m: Eliminate redundant objective function calls (patch #8073).
Ken Marek <gm.kmarek@gmail.com>
parents: 25054
diff changeset
460 c_new = feval (obj_grd, x_new, obj_new);
34cc6edf2041 sqp.m: Eliminate redundant objective function calls (patch #8073).
Ken Marek <gm.kmarek@gmail.com>
parents: 25054
diff changeset
461 endif
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
462
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
463 ce_new = feval (ce_fun, x_new);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
464 F_new = feval (ce_grd, x_new);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
465
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
466 ci_new = feval (ci_fun, x_new);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
467 C_new = feval (ci_grd, x_new);
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
468
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
469 A_new = [F_new; C_new];
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
470
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
471 ## Set
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
472 ##
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
473 ## s = alpha * p
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
474 ## y = grad_x L (x_new, lambda) - grad_x L (x, lambda})
6527
2a04f026ef54 [project @ 2007-04-16 16:54:09 by jwe]
jwe
parents: 6382
diff changeset
475
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
476 y = c_new - c;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
477
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
478 if (! isempty (A))
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
479 t = ((A_new - A)'*lambda);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
480 y -= t;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
481 endif
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
482
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
483 if (have_hess)
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
484
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
485 B = feval (obj_hess, x);
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
486
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
487 else
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
488 ## Update B using a quasi-Newton formula.
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
489 delxt = delx';
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
490
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
491 ## Damped BFGS. Or maybe we would actually want to use the Hessian
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
492 ## of the Lagrangian, computed directly?
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
493 d1 = delxt*B*delx;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
494
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
495 t1 = 0.2 * d1;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
496 t2 = delxt*y;
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
497
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
498 if (t2 < t1)
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
499 theta = 0.8*d1/(d1 - t2);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
500 else
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
501 theta = 1;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
502 endif
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
503
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
504 r = theta*y + (1-theta)*B*delx;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
505
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
506 d2 = delxt*r;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
507
18255
f58a6cd3f909 sqp.m: Fix return values in sqp (bug #32008).
Arun Giridhar <arungiridhar@gmail.com>
parents: 17744
diff changeset
508 ## Check if the next BFGS update will work properly.
f58a6cd3f909 sqp.m: Fix return values in sqp (bug #32008).
Arun Giridhar <arungiridhar@gmail.com>
parents: 17744
diff changeset
509 ## If d1 or d2 vanish, the BFGS update will fail.
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
510 if (d1 == 0 || d2 == 0)
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
511 info = 102;
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10542
diff changeset
512 break;
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
513 endif
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
514
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
515 B = B - B*delx*delxt*B/d1 + r*r'/d2;
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
516
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
517 endif
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
518
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
519 x = x_new;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
520
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
521 obj = obj_new;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
522
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
523 c = c_new;
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
524
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
525 ce = ce_new;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
526 F = F_new;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
527
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
528 ci = ci_new;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
529 C = C_new;
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
530
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
531 A = A_new;
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
532
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
533 # report (iter, qp_iter, alpha, __sqp_nfun__, obj);
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
534
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
535 endwhile
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
536
18255
f58a6cd3f909 sqp.m: Fix return values in sqp (bug #32008).
Arun Giridhar <arungiridhar@gmail.com>
parents: 17744
diff changeset
537 ## Check if we've spent too many iterations without converging.
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
538 if (iter >= iter_max)
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
539 info = 103;
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
540 endif
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
541
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
542 nf = globals.nfun;
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
543
7399
c1a3d6c7d2fb [project @ 2008-01-18 07:37:35 by jwe]
jwe
parents: 7381
diff changeset
544 endfunction
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
545
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
546
17245
7babcdb9bc13 Use ... instead of \ for line continuation marker.
Stefan Mahr <dac922@gmx.de>
parents: 17174
diff changeset
547 function [merit, obj, globals] = phi_L1 (obj, obj_fun, ce_fun, ci_fun, ...
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
548 x, mu, globals)
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
549
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
550 ce = feval (ce_fun, x);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
551 ci = feval (ci_fun, x);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
552
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
553 idx = ci < 0;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
554
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
555 con = [ce; ci(idx)];
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
556
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
557 if (isempty (obj))
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
558 obj = feval (obj_fun, x);
20735
418ae0cb752f Replace ++,-- with in-place operators for performance.
Rik <rik@octave.org>
parents: 20165
diff changeset
559 globals.nfun += 1;
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
560 endif
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
561
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
562 merit = obj;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
563 t = norm (con, 1) / mu;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
564
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
565 if (! isempty (t))
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
566 merit += t;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
567 endif
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
568
7399
c1a3d6c7d2fb [project @ 2008-01-18 07:37:35 by jwe]
jwe
parents: 7381
diff changeset
569 endfunction
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
570
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
571
17245
7babcdb9bc13 Use ... instead of \ for line continuation marker.
Stefan Mahr <dac922@gmx.de>
parents: 17174
diff changeset
572 function [x_new, alpha, obj, globals] = ...
26237
34cc6edf2041 sqp.m: Eliminate redundant objective function calls (patch #8073).
Ken Marek <gm.kmarek@gmail.com>
parents: 25054
diff changeset
573 linesearch_L1 (x, p, obj_fun, obj_grd, ce_fun, ci_fun, lambda, obj, c, globals)
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
574
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
575 ## Choose parameters
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
576 ##
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
577 ## eta in the range (0, 0.5)
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
578 ## tau in the range (0, 1)
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
579
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
580 eta = 0.25;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
581 tau = 0.5;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
582
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
583 delta_bar = sqrt (eps);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
584
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
585 if (isempty (lambda))
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
586 mu = 1 / delta_bar;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
587 else
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
588 mu = 1 / (norm (lambda, Inf) + delta_bar);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
589 endif
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
590
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
591 alpha = 1;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
592
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
593 ce = feval (ce_fun, x);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
594
17245
7babcdb9bc13 Use ... instead of \ for line continuation marker.
Stefan Mahr <dac922@gmx.de>
parents: 17174
diff changeset
595 [phi_x_mu, obj, globals] = phi_L1 (obj, obj_fun, ce_fun, ci_fun, x, ...
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
596 mu, globals);
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
597
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
598 D_phi_x_mu = c' * p;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
599 d = feval (ci_fun, x);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
600 ## only those elements of d corresponding
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
601 ## to violated constraints should be included.
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
602 idx = d < 0;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
603 t = - norm ([ce; d(idx)], 1) / mu;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
604 if (! isempty (t))
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
605 D_phi_x_mu += t;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
606 endif
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
607
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
608 while (1)
17245
7babcdb9bc13 Use ... instead of \ for line continuation marker.
Stefan Mahr <dac922@gmx.de>
parents: 17174
diff changeset
609 [p1, obj, globals] = phi_L1 ([], obj_fun, ce_fun, ci_fun, ...
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
610 x+alpha*p, mu, globals);
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
611 p2 = phi_x_mu+eta*alpha*D_phi_x_mu;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
612 if (p1 > p2)
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
613 ## Reset alpha = tau_alpha * alpha for some tau_alpha in the
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
614 ## range (0, tau).
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
615 tau_alpha = 0.9 * tau; # ??
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
616 alpha = tau_alpha * alpha;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
617 else
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
618 break;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
619 endif
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
620 endwhile
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
621
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
622 x_new = x + alpha * p;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
623
7399
c1a3d6c7d2fb [project @ 2008-01-18 07:37:35 by jwe]
jwe
parents: 7381
diff changeset
624 endfunction
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
625
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
626
26237
34cc6edf2041 sqp.m: Eliminate redundant objective function calls (patch #8073).
Ken Marek <gm.kmarek@gmail.com>
parents: 25054
diff changeset
627 function grd = fdgrd (f, x, y0)
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
628
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
629 if (! isempty (f))
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
630 nx = length (x);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
631 grd = zeros (nx, 1);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
632 deltax = sqrt (eps);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
633 for i = 1:nx
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
634 t = x(i);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
635 x(i) += deltax;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
636 grd(i) = (feval (f, x) - y0) / deltax;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
637 x(i) = t;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
638 endfor
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
639 else
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
640 grd = zeros (0, 1);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
641 endif
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
642
7399
c1a3d6c7d2fb [project @ 2008-01-18 07:37:35 by jwe]
jwe
parents: 7381
diff changeset
643 endfunction
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
644
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
645
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
646 function jac = fdjac (f, x)
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
647
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
648 nx = length (x);
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
649 if (! isempty (f))
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
650 y0 = feval (f, x);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
651 nf = length (y0);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
652 nx = length (x);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
653 jac = zeros (nf, nx);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
654 deltax = sqrt (eps);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
655 for i = 1:nx
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
656 t = x(i);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
657 x(i) += deltax;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
658 jac(:,i) = (feval (f, x) - y0) / deltax;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
659 x(i) = t;
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
660 endfor
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
661 else
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
662 jac = zeros (0, nx);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
663 endif
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
664
7399
c1a3d6c7d2fb [project @ 2008-01-18 07:37:35 by jwe]
jwe
parents: 7381
diff changeset
665 endfunction
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
666
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
667
26237
34cc6edf2041 sqp.m: Eliminate redundant objective function calls (patch #8073).
Ken Marek <gm.kmarek@gmail.com>
parents: 25054
diff changeset
668 function grd = fd_obj_grd (x, obj, obj_fun)
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
669
26237
34cc6edf2041 sqp.m: Eliminate redundant objective function calls (patch #8073).
Ken Marek <gm.kmarek@gmail.com>
parents: 25054
diff changeset
670 grd = fdgrd (obj_fun, x, obj);
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
671
7399
c1a3d6c7d2fb [project @ 2008-01-18 07:37:35 by jwe]
jwe
parents: 7381
diff changeset
672 endfunction
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
673
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
674
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
675 function res = empty_cf (x)
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
676
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
677 res = zeros (0, 1);
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
678
7399
c1a3d6c7d2fb [project @ 2008-01-18 07:37:35 by jwe]
jwe
parents: 7381
diff changeset
679 endfunction
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
680
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
681
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
682 function res = empty_jac (x)
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
683
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
684 res = zeros (0, length (x));
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
685
7399
c1a3d6c7d2fb [project @ 2008-01-18 07:37:35 by jwe]
jwe
parents: 7381
diff changeset
686 endfunction
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
687
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
688
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
689 function jac = fd_ce_jac (x, ce_fun)
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
690
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
691 jac = fdjac (ce_fun, x);
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
692
7399
c1a3d6c7d2fb [project @ 2008-01-18 07:37:35 by jwe]
jwe
parents: 7381
diff changeset
693 endfunction
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
694
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
695
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
696 function jac = fd_ci_jac (x, cifcn)
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
697
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
698 ## cifcn = constraint function without gradients and lb or ub
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
699 jac = fdjac (cifcn, x);
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
700
7399
c1a3d6c7d2fb [project @ 2008-01-18 07:37:35 by jwe]
jwe
parents: 7381
diff changeset
701 endfunction
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
702
7017
a1dbe9d80eee [project @ 2007-10-12 21:27:11 by jwe]
jwe
parents: 7016
diff changeset
703
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
704 function res = cf_ub_lb (x, lbidx, ubidx, globals)
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
705
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
706 ## combine constraint function with ub and lb
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
707 if (isempty (globals.cifcn))
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
708 res = [x(lbidx,1)-globals.lb; globals.ub-x(ubidx,1)];
11347
2726132f77f6 sqp.m: Remove never violated Inf bounds from computation (bug #31742)
Rik <octave@nomad.inbox5.com>
parents: 11290
diff changeset
709 else
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
710 res = [feval(globals.cifcn,x); x(lbidx,1)-globals.lb;
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
711 globals.ub-x(ubidx,1)];
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
712 endif
5289
b98bf1d70a0a [project @ 2005-04-21 14:43:14 by jwe]
jwe
parents:
diff changeset
713
7399
c1a3d6c7d2fb [project @ 2008-01-18 07:37:35 by jwe]
jwe
parents: 7381
diff changeset
714 endfunction
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
715
7017
a1dbe9d80eee [project @ 2007-10-12 21:27:11 by jwe]
jwe
parents: 7016
diff changeset
716
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
717 function res = cigrad_ub_lb (x, bgrad, globals)
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
718
19833
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 19697
diff changeset
719 cigradfcn = @(x) fd_ci_jac (x, globals.cifcn);
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
720
14595
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
721 if (iscell (globals.cif) && length (globals.cif) > 1)
11a9d448fdc3 Get rid of global variables in sqp.
Olaf Till <i7tiol@t-online.de>
parents: 14552
diff changeset
722 cigradfcn = globals.cif{2};
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
723 endif
11587
c792872f8942 all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
724
11347
2726132f77f6 sqp.m: Remove never violated Inf bounds from computation (bug #31742)
Rik <octave@nomad.inbox5.com>
parents: 11290
diff changeset
725 if (isempty (cigradfcn))
2726132f77f6 sqp.m: Remove never violated Inf bounds from computation (bug #31742)
Rik <octave@nomad.inbox5.com>
parents: 11290
diff changeset
726 res = bgrad;
2726132f77f6 sqp.m: Remove never violated Inf bounds from computation (bug #31742)
Rik <octave@nomad.inbox5.com>
parents: 11290
diff changeset
727 else
2726132f77f6 sqp.m: Remove never violated Inf bounds from computation (bug #31742)
Rik <octave@nomad.inbox5.com>
parents: 11290
diff changeset
728 res = [feval(cigradfcn,x); bgrad];
6768
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
729 endif
40e1255eda0e [project @ 2007-06-29 20:11:58 by jwe]
jwe
parents: 6741
diff changeset
730
7399
c1a3d6c7d2fb [project @ 2008-01-18 07:37:35 by jwe]
jwe
parents: 7381
diff changeset
731 endfunction
7361
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
732
19833
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 19697
diff changeset
733 ## Utility function used to debug sqp
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
734 function report (iter, qp_iter, alpha, nfun, obj)
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
735
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
736 if (nargin == 0)
21634
96518f623c91 Backed out changeset dcf8922b724b
Mike Miller <mtmiller@octave.org>
parents: 21633
diff changeset
737 printf (" Itn ItQP Step Nfun Objective\n");
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
738 else
21634
96518f623c91 Backed out changeset dcf8922b724b
Mike Miller <mtmiller@octave.org>
parents: 21633
diff changeset
739 printf ("%5d %4d %8.1g %5d %13.6e\n", iter, qp_iter, alpha, nfun, obj);
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
740 endif
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
741
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
742 endfunction
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
743
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
744
19833
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 19697
diff changeset
745 ################################################################################
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 19697
diff changeset
746 ## Test Code
11348
2ae0ca4ee36b sqp.m: Change docstring to refer to x0 as the initial seed vector
Rik <octave@nomad.inbox5.com>
parents: 11347
diff changeset
747
13305
63463570d9fe Add %!endfunction block keyword to test.m
Rik <octave@nomad.inbox5.com>
parents: 13268
diff changeset
748 %!function r = __g (x)
7371
fe9a44d753d6 [project @ 2008-01-14 19:34:22 by jwe]
jwe
parents: 7361
diff changeset
749 %! r = [sumsq(x)-10;
fe9a44d753d6 [project @ 2008-01-14 19:34:22 by jwe]
jwe
parents: 7361
diff changeset
750 %! x(2)*x(3)-5*x(4)*x(5);
fe9a44d753d6 [project @ 2008-01-14 19:34:22 by jwe]
jwe
parents: 7361
diff changeset
751 %! x(1)^3+x(2)^3+1 ];
13305
63463570d9fe Add %!endfunction block keyword to test.m
Rik <octave@nomad.inbox5.com>
parents: 13268
diff changeset
752 %!endfunction
7361
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
753 %!
13305
63463570d9fe Add %!endfunction block keyword to test.m
Rik <octave@nomad.inbox5.com>
parents: 13268
diff changeset
754 %!function obj = __phi (x)
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
755 %! obj = exp (prod (x)) - 0.5*(x(1)^3 + x(2)^3 + 1)^2;
13305
63463570d9fe Add %!endfunction block keyword to test.m
Rik <octave@nomad.inbox5.com>
parents: 13268
diff changeset
756 %!endfunction
7361
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
757 %!
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
758 %!test
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
759 %!
7361
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
760 %! x0 = [-1.8; 1.7; 1.9; -0.8; -0.8];
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
761 %!
13305
63463570d9fe Add %!endfunction block keyword to test.m
Rik <octave@nomad.inbox5.com>
parents: 13268
diff changeset
762 %! [x, obj, info, iter, nf, lambda] = sqp (x0, @__phi, @__g, []);
7361
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
763 %!
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
764 %! x_opt = [-1.717143501952599;
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
765 %! 1.595709610928535;
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
766 %! 1.827245880097156;
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
767 %! -0.763643103133572;
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
768 %! -0.763643068453300];
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
769 %!
7371
fe9a44d753d6 [project @ 2008-01-14 19:34:22 by jwe]
jwe
parents: 7361
diff changeset
770 %! obj_opt = 0.0539498477702739;
7361
a2870fd8ac58 [project @ 2008-01-12 07:50:54 by jwe]
jwe
parents: 7031
diff changeset
771 %!
15757
534a2c881f45 Increase test tolerance on sqp (bug #37742)
Mike Miller <mtmiller@ieee.org>
parents: 14868
diff changeset
772 %! assert (x, x_opt, 8*sqrt (eps));
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
773 %! assert (obj, obj_opt, sqrt (eps));
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
774
19833
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 19697
diff changeset
775 ## Test input validation
10678
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
776 %!error sqp ()
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
777 %!error sqp (1)
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
778 %!error sqp (1,2,3,4,5,6,7,8,9)
35338deff753 Guarantee equivalent results if sqp called with or wihout bounds
Rik <octave@nomad.inbox5.com>
parents: 10549
diff changeset
779 %!error sqp (1,2,3,4,5)
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
780 %!error sqp (ones (2,2))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
781 %!error sqp (1, cell (4,1))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
782 %!error sqp (1, cell (3,1), cell (3,1))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
783 %!error sqp (1, cell (3,1), cell (2,1), cell (3,1))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
784 %!error sqp (1, cell (3,1), cell (2,1), cell (2,1), ones (2,2),[])
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
785 %!error sqp (1, cell (3,1), cell (2,1), cell (2,1),[], ones (2,2))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
786 %!error sqp (1, cell (3,1), cell (2,1), cell (2,1),1,-1)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
787 %!error sqp (1, cell (3,1), cell (2,1), cell (2,1),[],[], ones (2,2))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
788 %!error sqp (1, cell (3,1), cell (2,1), cell (2,1),[],[],-1)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
789 %!error sqp (1, cell (3,1), cell (2,1), cell (2,1),[],[],1.5)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
790 %!error sqp (1, cell (3,1), cell (2,1), cell (2,1),[],[],[], ones (2,2))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
791 %!error sqp (1, cell (3,1), cell (2,1), cell (2,1),[],[],[],-1)