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+// This is an example for unconstraint nonlinear problems.
+//Ref:J. J. More, B. S. Garbow, and K. E. Hillstrom, Testing unconstrained optimization software, ACM Transactions on Mathematical Software, Vol. 7, No. 1, pp. 17–41, 1981.
+//Example:
+//f(x1,x2) = (x1 - 10^6)^2 + (x2 - 2*10^-6)^2 + (x1*x2 - 2)^2;
+//======================================================================
+// 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:Debasis Maharana
+// Organization: FOSSEE, IIT Bombay
+// Email: toolbox@scilab.in
+//======================================================================
+clc;close
+
+function y = Brownsfunc(x)
+ y = (x(1)-1d6)^2 + (x(2)-2*1D-6)^2 + (x(1)*x(2)-2)^2
+endfunction
+
+function stop=outfun(x, optimValues, state)
+ subplot(1,2,1)
+ plot(optimValues.funccount,optimValues.fval,'r.');
+ xlabel('function count');ylabel('Objective value')
+
+ subplot(1,2,2)
+ plot(optimValues.funccount,x(1),'r.');
+ plot(optimValues.funccount,x(2),'b.');
+ legend(['X1','X2'])
+ set(gca(),"auto_clear","off")
+ xlabel('function count');ylabel('variable values')
+
+ stop = %f
+endfunction
+
+X0 = [1 1];
+MFes = 500;
+Miter = 200;
+TF = 1D-6;
+TX = 1D-6;
+mprintf('The following settings are used\n Maximum iterations %d \n maximum functional exaluations %d\n Function tolerance %s \n variable tolerance %s ',Miter,MFes,string(TF),string(TX));
+mprintf('\nThe initial guess is x1 = %f and x2 = %f',X0(1),X0(2))
+input('Press enter to proceed ')
+clc;
+mprintf('Scilab is solving the problem...')
+
+options = optimset ("MaxFunEvals",MFes,"MaxIter",Miter,"TolFun",TF,"TolX",TX, "OutputFcn" , outfun);
+
+[x,fval,exitflag,output] = fminsearch(Brownsfunc,X0,options)
+
+clc
+select exitflag
+case -1
+ disp(output.algorithm, 'Algorithm used')
+ mprintf('\n The maximum number of iterations has been reached \n')
+ mprintf('\n The number of iterations %d ',output.iterations)
+ mprintf('\n The number of function evaluations %d',output.funcCount)
+case 0
+ disp(output.algorithm, 'Algorithm used ')
+ mprintf('\n The maximum number of function evaluations has been reached \n')
+ mprintf('\n The number of function evaluations %d',output.funcCount)
+ mprintf('\n The number of iterations %d ',output.iterations)
+
+case 1
+ disp(output.algorithm, 'Algorithm used ')
+ mprintf('\n The tolerance on the simplex size and function value delta has been reached\n')
+ mprintf('\n The number of function evaluations %d',output.funcCount)
+ mprintf('\n The number of iterations %d ',output.iterations)
+end
+
+disp(x,"The optimal solution is")
+mprintf("\n The optimum value of the function is %s",string(fval))