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authorRemyaDebasis2018-07-23 20:08:46 +0530
committerRemyaDebasis2018-07-23 20:08:46 +0530
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+// J.Hald, K Madsen, Reference:Combined LP and quasi-Newton methos for minimax optimization, Mathematical Programming, Springer, 1981
+// Min F = max|fi(x)|
+// fi(X) = (X1 + X2*ti - exp(ti))^2 + (X3 + X4*sin(ti) - cos(ti))^2 where i varies from 1 to 20
+// ti = 0.2i
+// Global optima: X* = [-12.24368 14.02180 -0.45151 -0.01052]; F* = 115.70644;
+//======================================================================
+// Copyright (C) 2018 - IIT Bombay - FOSSEE
+// This file must be used under the terms of the CeCILL.
+// This source file is licensed as described in the file COPYING, which
+// you should have received as part of this distribution. The terms
+// are also available at
+// http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+// Author: Remya Kommadath
+// Organization: FOSSEE, IIT Bombay
+// Email: toolbox@scilab.in
+//======================================================================
+clc;
+// Objective function
+function f = ObjectiveFunction(X)
+ m = 20;
+ for i = 1:m
+ t(i) = 0.2*i;
+ f(i) = abs((X(1) + X(2)*t(i) - exp(t(i)))^2 + (X(3) + X(4)*sin(t(i)) - cos(t(i)))^2);
+ end
+endfunction
+// Initial guess to the solver
+x0 = [-10 5 1 -2]
+
+// Run fminimax
+options= list("MaxIter", 10000);
+[x,fval,maxfval,exitflag,output,lambda] = fminimax(ObjectiveFunction,x0,[],[],[],[],[],[],[],options);
+
+// Result representation
+clc;
+select exitflag
+case 0
+ disp("Optimal Solution Found")
+ disp(x0,"The initial guess given to the solver")
+ disp(x',"The optimal solution determined by the solver")
+ disp(maxfval,"The optimum value of the objective function")
+case 1
+ disp("Maximum Number of Iterations Exceeded. Output may not be optimal")
+case 2
+ disp("Maximum amount of CPU Time exceeded. Output may not be optimal")
+case 3
+ disp("Stop at Tiny Step")
+case 4
+ disp("Solved To Acceptable Level")
+case 5
+ disp("Converged to a point of local infeasibility")
+end
+