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Diffstat (limited to 'help/en_US/scilab_en_US_help/fminimax.html')
| -rw-r--r-- | help/en_US/scilab_en_US_help/fminimax.html | 92 |
1 files changed, 45 insertions, 47 deletions
diff --git a/help/en_US/scilab_en_US_help/fminimax.html b/help/en_US/scilab_en_US_help/fminimax.html index 2d086ff..a701aa7 100644 --- a/help/en_US/scilab_en_US_help/fminimax.html +++ b/help/en_US/scilab_en_US_help/fminimax.html @@ -16,7 +16,7 @@ </td> <td width="40%" class="center"> - <span class="top"><a href="section_19f4f1e5726c01d683e8b82be0a7e910.html">Symphony Toolbox</a></span> + <span class="top"><a href="section_19f4f1e5726c01d683e8b82be0a7e910.html">FOSSEE Optimization Toolbox</a></span> </td> <td width="30%" class="next"> @@ -29,7 +29,7 @@ - <span class="path"><a href="index.html">Symphony Toolbox</a> >> <a href="section_19f4f1e5726c01d683e8b82be0a7e910.html">Symphony Toolbox</a> > fminimax</span> + <span class="path"><a href="index.html">FOSSEE Optimization Toolbox</a> >> <a href="section_19f4f1e5726c01d683e8b82be0a7e910.html">FOSSEE Optimization Toolbox</a> > fminimax</span> <br /><br /> <div class="refnamediv"><h1 class="refname">fminimax</h1> @@ -37,51 +37,49 @@ <div class="refsynopsisdiv"><h3 class="title">Calling Sequence</h3> - <div class="synopsis"><pre><span class="default">x</span><span class="default"> = </span><span class="functionid">fminimax</span><span class="default">(</span><span class="default">fun</span><span class="default">,</span><span class="default">x0</span><span class="default">)</span> -<span class="default">x</span><span class="default"> = </span><span class="functionid">fminimax</span><span class="default">(</span><span class="default">fun</span><span class="default">,</span><span class="default">x0</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">)</span> -<span class="default">x</span><span class="default"> = </span><span class="functionid">fminimax</span><span class="default">(</span><span class="default">fun</span><span class="default">,</span><span class="default">x0</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">)</span> -<span class="default">x</span><span class="default"> = </span><span class="functionid">fminimax</span><span class="default">(</span><span class="default">fun</span><span class="default">,</span><span class="default">x0</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">,</span><span class="default">lb</span><span class="default">,</span><span class="default">ub</span><span class="default">)</span> -<span class="default">x</span><span class="default"> = </span><span class="functionid">fminimax</span><span class="default">(</span><span class="default">fun</span><span class="default">,</span><span class="default">x0</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">,</span><span class="default">lb</span><span class="default">,</span><span class="default">ub</span><span class="default">,</span><span class="default">nonlinfun</span><span class="default">)</span> -<span class="default">x</span><span class="default"> = </span><span class="functionid">fminimax</span><span class="default">(</span><span class="default">fun</span><span class="default">,</span><span class="default">x0</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">,</span><span class="default">lb</span><span class="default">,</span><span class="default">ub</span><span class="default">,</span><span class="default">nonlinfun</span><span class="default">,</span><span class="default">options</span><span class="default">)</span> -<span class="default">[</span><span class="default">x</span><span class="default">, </span><span class="default">fval</span><span class="default">] = </span><span class="default">fmincon</span><span class="default">(.....)</span> -<span class="default">[</span><span class="default">x</span><span class="default">, </span><span class="default">fval</span><span class="default">, </span><span class="default">maxfval</span><span class="default">]= </span><span class="default">fmincon</span><span class="default">(.....)</span> -<span class="default">[</span><span class="default">x</span><span class="default">, </span><span class="default">fval</span><span class="default">, </span><span class="default">maxfval</span><span class="default">, </span><span class="default">exitflag</span><span class="default">]= </span><span class="default">fmincon</span><span class="default">(.....)</span> -<span class="default">[</span><span class="default">x</span><span class="default">, </span><span class="default">fval</span><span class="default">, </span><span class="default">maxfval</span><span class="default">, </span><span class="default">exitflag</span><span class="default">, </span><span class="default">output</span><span class="default">]= </span><span class="default">fmincon</span><span class="default">(.....)</span> -<span class="default">[</span><span class="default">x</span><span class="default">, </span><span class="default">fval</span><span class="default">, </span><span class="default">maxfval</span><span class="default">, </span><span class="default">exitflag</span><span class="default">, </span><span class="default">output</span><span class="default">, </span><span class="default">lambda</span><span class="default">]= </span><span class="default">fmincon</span><span class="default">(.....)</span></pre></div></div> + <div class="synopsis"><pre><span class="default">xopt</span><span class="default"> = </span><span class="functionid">fminimax</span><span class="default">(</span><span class="default">fun</span><span class="default">,</span><span class="default">x0</span><span class="default">)</span> +<span class="default">xopt</span><span class="default"> = </span><span class="functionid">fminimax</span><span class="default">(</span><span class="default">fun</span><span class="default">,</span><span class="default">x0</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">)</span> +<span class="default">xopt</span><span class="default"> = </span><span class="functionid">fminimax</span><span class="default">(</span><span class="default">fun</span><span class="default">,</span><span class="default">x0</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">)</span> +<span class="default">xopt</span><span class="default"> = </span><span class="functionid">fminimax</span><span class="default">(</span><span class="default">fun</span><span class="default">,</span><span class="default">x0</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">,</span><span class="default">lb</span><span class="default">,</span><span class="default">ub</span><span class="default">)</span> +<span class="default">xopt</span><span class="default"> = </span><span class="functionid">fminimax</span><span class="default">(</span><span class="default">fun</span><span class="default">,</span><span class="default">x0</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">,</span><span class="default">lb</span><span class="default">,</span><span class="default">ub</span><span class="default">,</span><span class="default">nonlinfun</span><span class="default">)</span> +<span class="default">xopt</span><span class="default"> = </span><span class="functionid">fminimax</span><span class="default">(</span><span class="default">fun</span><span class="default">,</span><span class="default">x0</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">,</span><span class="default">lb</span><span class="default">,</span><span class="default">ub</span><span class="default">,</span><span class="default">nonlinfun</span><span class="default">,</span><span class="default">options</span><span class="default">)</span> +<span class="default">[</span><span class="default">xopt</span><span class="default">, </span><span class="default">fval</span><span class="default">] = </span><span class="default">fmincon</span><span class="default">(.....)</span> +<span class="default">[</span><span class="default">xopt</span><span class="default">, </span><span class="default">fval</span><span class="default">, </span><span class="default">maxfval</span><span class="default">]= </span><span class="default">fmincon</span><span class="default">(.....)</span> +<span class="default">[</span><span class="default">xopt</span><span class="default">, </span><span class="default">fval</span><span class="default">, </span><span class="default">maxfval</span><span class="default">, </span><span class="default">exitflag</span><span class="default">]= </span><span class="default">fmincon</span><span class="default">(.....)</span> +<span class="default">[</span><span class="default">xopt</span><span class="default">, </span><span class="default">fval</span><span class="default">, </span><span class="default">maxfval</span><span class="default">, </span><span class="default">exitflag</span><span class="default">, </span><span class="default">output</span><span class="default">]= </span><span class="default">fmincon</span><span class="default">(.....)</span> +<span class="default">[</span><span class="default">xopt</span><span class="default">, </span><span class="default">fval</span><span class="default">, </span><span class="default">maxfval</span><span class="default">, </span><span class="default">exitflag</span><span class="default">, </span><span class="default">output</span><span class="default">, </span><span class="default">lambda</span><span class="default">]= </span><span class="default">fmincon</span><span class="default">(.....)</span></pre></div></div> <div class="refsection"><h3 class="title">Parameters</h3> <dl><dt><span class="term">fun:</span> <dd><p class="para">The function to be minimized. fun is a function that accepts a vector x and returns a vector F, the objective functions evaluated at x.</p></dd></dt> - <dt><span class="term">x0:</span> - <dd><p class="para">a nx1 or 1xn matrix of doubles, where n is the number of variables, the initial guess for the optimization algorithm</p></dd></dt> - <dt><span class="term">A:</span> - <dd><p class="para">a nil x n matrix of doubles, where n is the number of variables and nil is the number of linear inequalities. If A==[] and b==[], it is assumed that there is no linear inequality constraints. If (A==[] & b<>[]), fminimax generates an error (the same happens if (A<>[] & b==[]))</p></dd></dt> - <dt><span class="term">b:</span> - <dd><p class="para">a nil x 1 matrix of doubles, where nil is the number of linear inequalities</p></dd></dt> - <dt><span class="term">Aeq:</span> - <dd><p class="para">a nel x n matrix of doubles, where n is the number of variables and nel is the number of linear equalities. If Aeq==[] and beq==[], it is assumed that there is no linear equality constraints. If (Aeq==[] & beq<>[]), fminimax generates an error (the same happens if (Aeq<>[] & beq==[]))</p></dd></dt> - <dt><span class="term">beq:</span> - <dd><p class="para">a nel x 1 matrix of doubles, where nel is the number of linear equalities</p></dd></dt> - <dt><span class="term">lb:</span> - <dd><p class="para">a nx1 or 1xn matrix of doubles, where n is the number of variables. The lower bound for x. If lb==[], then the lower bound is automatically set to -inf</p></dd></dt> - <dt><span class="term">ub:</span> - <dd><p class="para">a nx1 or 1xn matrix of doubles, where n is the number of variables. The upper bound for x. If ub==[], then the upper bound is automatically set to +inf</p></dd></dt> + <dt><span class="term">x0 :</span> + <dd><p class="para">a vector of double, contains initial guess of variables.</p></dd></dt> + <dt><span class="term">A :</span> + <dd><p class="para">a matrix of double, represents the linear coefficients in the inequality constraints A⋅x ≤ b.</p></dd></dt> + <dt><span class="term">b :</span> + <dd><p class="para">a vector of double, represents the linear coefficients in the inequality constraints A⋅x ≤ b.</p></dd></dt> + <dt><span class="term">Aeq :</span> + <dd><p class="para">a matrix of double, represents the linear coefficients in the equality constraints Aeq⋅x = beq.</p></dd></dt> + <dt><span class="term">beq :</span> + <dd><p class="para">a vector of double, represents the linear coefficients in the equality constraints Aeq⋅x = beq.</p></dd></dt> + <dt><span class="term">lb :</span> + <dd><p class="para">a vector of double, contains lower bounds of the variables.</p></dd></dt> + <dt><span class="term">ub :</span> + <dd><p class="para">a vector of double, contains upper bounds of the variables.</p></dd></dt> <dt><span class="term">nonlinfun:</span> - <dd><p class="para">function that computes the nonlinear inequality constraints c(x) <= 0 and nonlinear equality constraints ceq(x) = 0.</p></dd></dt> - <dt><span class="term">x:</span> - <dd><p class="para">a nx1 matrix of doubles, the computed solution of the optimization problem</p></dd></dt> - <dt><span class="term">fval:</span> - <dd><p class="para">a vector of doubles, the value of fun at x</p></dd></dt> + <dd><p class="para">function that computes the nonlinear inequality constraints c⋅x ≤ 0 and nonlinear equality constraints c⋅x = 0.</p></dd></dt> + <dt><span class="term">xopt :</span> + <dd><p class="para">a vector of double, the computed solution of the optimization problem.</p></dd></dt> + <dt><span class="term">fopt :</span> + <dd><p class="para">a double, the value of the function at x.</p></dd></dt> <dt><span class="term">maxfval:</span> <dd><p class="para">a 1x1 matrix of doubles, the maximum value in vector fval</p></dd></dt> - <dt><span class="term">exitflag:</span> - <dd><p class="para">a 1x1 matrix of floating point integers, the exit status</p></dd></dt> - <dt><span class="term">output:</span> - <dd><p class="para">a struct, the details of the optimization process</p></dd></dt> - <dt><span class="term">lambda:</span> - <dd><p class="para">a struct, the Lagrange multipliers at optimum</p></dd></dt> - <dt><span class="term">options:</span> - <dd><p class="para">a list, containing the option for user to specify. See below for details.</p></dd></dt></dl></div> + <dt><span class="term">exitflag :</span> + <dd><p class="para">The exit status. See below for details.</p></dd></dt> + <dt><span class="term">output :</span> + <dd><p class="para">The structure consist of statistics about the optimization. See below for details.</p></dd></dt> + <dt><span class="term">lambda :</span> + <dd><p class="para">The structure consist of the Lagrange multipliers at the solution of problem. See below for details.</p></dd></dt></dl></div> <div class="refsection"><h3 class="title">Description</h3> <p class="para">fminimax minimizes the worst-case (largest) value of a set of multivariable functions, starting at an initial estimate. This is generally referred to as the minimax problem.</p> @@ -157,11 +155,11 @@ It has type "struct" and contains the following fields. <span class="scilabcomment">// The initial guess</span> <span class="scilabid">x0</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">0.1</span><span class="scilabdefault">,</span><span class="scilabnumber">0.1</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> <span class="scilabcomment">// The expected solution : only 4 digits are guaranteed</span> -<span class="scilabcomment">//xopt = [4 4]</span> -<span class="scilabcomment">//fopt = [0 -64 -2 -8 0]</span> +<span class="scilabid">xopt</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">4</span> <span class="scilabnumber">4</span><span class="scilabopenclose">]</span> +<span class="scilabid">fopt</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">0</span> <span class="scilaboperator">-</span><span class="scilabnumber">64</span> <span class="scilaboperator">-</span><span class="scilabnumber">2</span> <span class="scilaboperator">-</span><span class="scilabnumber">8</span> <span class="scilabnumber">0</span><span class="scilabopenclose">]</span> <span class="scilabid">maxfopt</span> <span class="scilaboperator">=</span> <span class="scilabnumber">0</span> <span class="scilabcomment">// Run fminimax</span> -<span class="scilabopenclose">[</span><span class="scilabid">xopt</span><span class="scilabdefault">,</span><span class="scilabid">fopt</span><span class="scilabdefault">,</span><span class="scilabid">maxfval</span><span class="scilabdefault">,</span><span class="scilabid">exitflag</span><span class="scilabdefault">,</span><span class="scilabid">output</span><span class="scilabdefault">,</span><span class="scilabid">lambda</span><span class="scilabopenclose">]</span> <span class="scilaboperator">=</span> <span class="scilabid">fminimax</span><span class="scilabopenclose">(</span><span class="scilabfunctionid">myfun</span><span class="scilabdefault">,</span> <span class="scilabid">x0</span><span class="scilabopenclose">)</span> +<span class="scilabopenclose">[</span><span class="scilabid">x</span><span class="scilabdefault">,</span><span class="scilabid">fval</span><span class="scilabdefault">,</span><span class="scilabid">maxfval</span><span class="scilabdefault">,</span><span class="scilabid">exitflag</span><span class="scilabdefault">,</span><span class="scilabid">output</span><span class="scilabdefault">,</span><span class="scilabid">lambda</span><span class="scilabopenclose">]</span> <span class="scilaboperator">=</span> <span class="scilabid">fminimax</span><span class="scilabopenclose">(</span><span class="scilabfunctionid">myfun</span><span class="scilabdefault">,</span> <span class="scilabid">x0</span><span class="scilabopenclose">)</span> <span class="scilabcomment">// Press ENTER to continue</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div> <div class="refsection"><h3 class="title">Examples</h3> @@ -206,11 +204,11 @@ It has type "struct" and contains the following fields. <span class="scilabcomment">// The initial guess</span> <span class="scilabid">x0</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">10</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span> <span class="scilabcomment">// The expected solution : only 4 digits are guaranteed</span> -<span class="scilabcomment">//xopt = [0.92791 7.93551]</span> -<span class="scilabcomment">//fopt = [6.73443 -189.778 6.73443 -8.86342 0.86342]</span> +<span class="scilabid">xopt</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">0.92791</span> <span class="scilabnumber">7.93551</span><span class="scilabopenclose">]</span> +<span class="scilabid">fopt</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">6.73443</span> <span class="scilaboperator">-</span><span class="scilabnumber">189.778</span> <span class="scilabnumber">6.73443</span> <span class="scilaboperator">-</span><span class="scilabnumber">8.86342</span> <span class="scilabnumber">0.86342</span><span class="scilabopenclose">]</span> <span class="scilabid">maxfopt</span> <span class="scilaboperator">=</span> <span class="scilabnumber">6.73443</span> <span class="scilabcomment">// Run fminimax</span> -<span class="scilabopenclose">[</span><span class="scilabid">xopt</span><span class="scilabdefault">,</span><span class="scilabid">fopt</span><span class="scilabdefault">,</span><span class="scilabid">maxfval</span><span class="scilabdefault">,</span><span class="scilabid">exitflag</span><span class="scilabdefault">,</span><span class="scilabid">output</span><span class="scilabopenclose">]</span> <span class="scilaboperator">=</span> <span class="scilabid">fminimax</span><span class="scilabopenclose">(</span><span class="scilabfunctionid">myfun</span><span class="scilabdefault">,</span><span class="scilabid">x0</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span> <span class="scilabfunctionid">confun</span><span class="scilabdefault">,</span> <span class="scilabid">minimaxOptions</span><span class="scilabopenclose">)</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div> +<span class="scilabopenclose">[</span><span class="scilabid">x</span><span class="scilabdefault">,</span><span class="scilabid">fval</span><span class="scilabdefault">,</span><span class="scilabid">maxfval</span><span class="scilabdefault">,</span><span class="scilabid">exitflag</span><span class="scilabdefault">,</span><span class="scilabid">output</span><span class="scilabopenclose">]</span> <span class="scilaboperator">=</span> <span class="scilabid">fminimax</span><span class="scilabopenclose">(</span><span class="scilabfunctionid">myfun</span><span class="scilabdefault">,</span><span class="scilabid">x0</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span> <span class="scilabfunctionid">confun</span><span class="scilabdefault">,</span> <span class="scilabid">minimaxOptions</span><span class="scilabopenclose">)</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div> <div class="refsection"><h3 class="title">Authors</h3> <ul class="itemizedlist"><li class="member">Animesh Baranawal</li></ul></div> @@ -225,7 +223,7 @@ It has type "struct" and contains the following fields. </td> <td width="40%" class="center"> - <span class="top"><a href="section_19f4f1e5726c01d683e8b82be0a7e910.html">Symphony Toolbox</a></span> + <span class="top"><a href="section_19f4f1e5726c01d683e8b82be0a7e910.html">FOSSEE Optimization Toolbox</a></span> </td> <td width="30%" class="next"> |