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Diffstat (limited to 'macros/fminimax.sci')
| -rw-r--r-- | macros/fminimax.sci | 102 |
1 files changed, 35 insertions, 67 deletions
diff --git a/macros/fminimax.sci b/macros/fminimax.sci index 04d0af6..c775b1b 100644 --- a/macros/fminimax.sci +++ b/macros/fminimax.sci @@ -1,49 +1,47 @@ -// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab // Copyright (C) 2015 - IIT Bombay - FOSSEE // -// Authors: Animesh Baranawal -// Organization: FOSSEE, IIT Bombay -// Email: animeshbaranawal@gmail.com // 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 +// Authors: Animesh Baranawal +// Organization: FOSSEE, IIT Bombay +// Email: toolbox@scilab.in function [x,fval,maxfval,exitflag,output,lambda] = fminimax(varargin) // Solves minimax constraint problem // // Calling Sequence - // x = fminimax(fun,x0) - // x = fminimax(fun,x0,A,b) - // x = fminimax(fun,x0,A,b,Aeq,beq) - // x = fminimax(fun,x0,A,b,Aeq,beq,lb,ub) - // x = fminimax(fun,x0,A,b,Aeq,beq,lb,ub,nonlinfun) - // x = fminimax(fun,x0,A,b,Aeq,beq,lb,ub,nonlinfun,options) - // [x, fval] = fmincon(.....) - // [x, fval, maxfval]= fmincon(.....) - // [x, fval, maxfval, exitflag]= fmincon(.....) - // [x, fval, maxfval, exitflag, output]= fmincon(.....) - // [x, fval, maxfval, exitflag, output, lambda]= fmincon(.....) + // xopt = fminimax(fun,x0) + // xopt = fminimax(fun,x0,A,b) + // xopt = fminimax(fun,x0,A,b,Aeq,beq) + // xopt = fminimax(fun,x0,A,b,Aeq,beq,lb,ub) + // xopt = fminimax(fun,x0,A,b,Aeq,beq,lb,ub,nonlinfun) + // xopt = fminimax(fun,x0,A,b,Aeq,beq,lb,ub,nonlinfun,options) + // [xopt, fval] = fmincon(.....) + // [xopt, fval, maxfval]= fmincon(.....) + // [xopt, fval, maxfval, exitflag]= fmincon(.....) + // [xopt, fval, maxfval, exitflag, output]= fmincon(.....) + // [xopt, fval, maxfval, exitflag, output, lambda]= fmincon(.....) // // Parameters // fun: 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. - // x0: a nx1 or 1xn matrix of doubles, where n is the number of variables, the initial guess for the optimization algorithm - // A: 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==[])) - // b: a nil x 1 matrix of doubles, where nil is the number of linear inequalities - // Aeq: 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==[])) - // beq: a nel x 1 matrix of doubles, where nel is the number of linear equalities - // lb: 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 - // ub: 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 - // nonlinfun: function that computes the nonlinear inequality constraints c(x) <= 0 and nonlinear equality constraints ceq(x) = 0. - // x: a nx1 matrix of doubles, the computed solution of the optimization problem - // fval: a vector of doubles, the value of fun at x - // maxfval: a 1x1 matrix of doubles, the maximum value in vector fval - // exitflag: a 1x1 matrix of floating point integers, the exit status - // output: a struct, the details of the optimization process - // lambda: a struct, the Lagrange multipliers at optimum - // options: a list, containing the option for user to specify. See below for details. - // + // x0 : a vector of double, contains initial guess of variables. + // A : a matrix of double, represents the linear coefficients in the inequality constraints A⋅x ≤ b. + // b : a vector of double, represents the linear coefficients in the inequality constraints A⋅x ≤ b. + // Aeq : a matrix of double, represents the linear coefficients in the equality constraints Aeq⋅x = beq. + // beq : a vector of double, represents the linear coefficients in the equality constraints Aeq⋅x = beq. + // lb : a vector of double, contains lower bounds of the variables. + // ub : a vector of double, contains upper bounds of the variables. + // nonlinfun: function that computes the nonlinear inequality constraints c⋅x ≤ 0 and nonlinear equality constraints c⋅x = 0. + // xopt : a vector of double, the computed solution of the optimization problem. + // fopt : a double, the value of the function at x. + // maxfval: a 1x1 matrix of doubles, the maximum value in vector fval + // exitflag : The exit status. See below for details. + // output : The structure consist of statistics about the optimization. See below for details. + // lambda : The structure consist of the Lagrange multipliers at the solution of problem. See below for details. + // // Description // 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. // @@ -160,7 +158,6 @@ function [x,fval,maxfval,exitflag,output,lambda] = fminimax(varargin) // f(4)= -x(1) - x(2); // f(5)= x(1) + x(2) - 8; // endfunction - // // // The initial guess // x0 = [0.1,0.1]; // // The expected solution : only 4 digits are guaranteed @@ -169,6 +166,7 @@ function [x,fval,maxfval,exitflag,output,lambda] = fminimax(varargin) // maxfopt = 0 // // Run fminimax // [x,fval,maxfval,exitflag,output,lambda] = fminimax(myfun, x0) + // // Press ENTER to continue // // Examples // // A case where we provide the gradient of the objective @@ -181,14 +179,11 @@ function [x,fval,maxfval,exitflag,output,lambda] = fminimax(varargin) // f(4)= -x(1) - x(2); // f(5)= x(1) + x(2) - 8; // endfunction - // // // Defining gradient of myfun // function G = myfungrad(x) // G = [ 4*x(1) - 48, -2*x(1), 1, -1, 1; // 2*x(2) - 40, -6*x(2), 3, -1, 1; ]' // endfunction - // - // // // The nonlinear constraints and the Jacobian // // matrix of the constraints // function [c,ceq] = confun(x) @@ -197,8 +192,6 @@ function [x,fval,maxfval,exitflag,output,lambda] = fminimax(varargin) // // No nonlinear equality constraints // ceq=[] // endfunction - // - // // // Defining gradient of confungrad // function [DC,DCeq] = cgrad(x) // // DC(:,i) = gradient of the i-th constraint @@ -212,7 +205,6 @@ function [x,fval,maxfval,exitflag,output,lambda] = fminimax(varargin) // ]' // DCeq = []' // endfunction - // // // Test with both gradient of objective and gradient of constraints // minimaxOptions = list("GradObj",myfungrad,"GradCon",cgrad); // // The initial guess @@ -223,8 +215,6 @@ function [x,fval,maxfval,exitflag,output,lambda] = fminimax(varargin) // maxfopt = 6.73443 // // Run fminimax // [x,fval,maxfval,exitflag,output] = fminimax(myfun,x0,[],[],[],[],[],[], confun, minimaxOptions) - // - // // Authors // Animesh Baranawal // @@ -377,14 +367,14 @@ function [x,fval,maxfval,exitflag,output,lambda] = fminimax(varargin) //To check the User Entry for Options and storing it for i = 1:(size(minmaxUserOptions))/2 - select minmaxUserOptions(2*i-1) - case "MaxIter" then + select convstr(minmaxUserOptions(2*i-1),'l') + case "maxiter" then minmaxIter = minmaxUserOptions(2*i); //Setting the Maximum Iteration as per user entry - case "CpuTime" then + case "cputime" then minmaxCPU = minmaxUserOptions(2*i); //Setting the Maximum CPU Time as per user entry - case "GradObj" then + case "gradobj" then if (type(minmaxUserOptions(2*i))==10) then if (convstr(minmaxUserOptions(2*i))=="off") then flag1 = 0; @@ -397,7 +387,7 @@ function [x,fval,maxfval,exitflag,output,lambda] = fminimax(varargin) minmaxFGrad = minmaxUserOptions(2*i); end - case "GradCon" then + case "gradcon" then if (type(minmaxUserOptions(2*i))==10) then if (convstr(minmaxUserOptions(2*i))=="off") then flag2 = 0; @@ -515,27 +505,6 @@ function [x,fval,maxfval,exitflag,output,lambda] = fminimax(varargin) end endfunction - // disp(minmaxStartpoint) - // a = minmaxObjfun(minmaxStartpoint) - // disp(a) - // disp(newObjfun(minmaxStartpoint)) - // disp(minmaxA) - // disp(minmaxB) - // disp(minmaxAeq) - // disp(minmaxBeq) - // disp(minmaxLb) - // disp(minmaxUb) - // [a,b] = minmaxNonlinfun(minmaxStartpoint) - // disp(a) - // disp(b) - // [a,b] = newNonlinfun(minmaxStartpoint) - // disp(a) - // disp(b) - // [a,b] = newCGrad(minmaxStartpoint) - // disp(a) - // disp(b) - // disp(newFGrad(minmaxStartpoint)) - // to be passed as minimaxOptions to fmincon if(flag1 == 1 | flag2 == 1) then minmaxPassOptions = list("MaxIter", minmaxMaxIter, "CpuTime", minmaxCPU, "GradCon", newCGrad) @@ -555,5 +524,4 @@ function [x,fval,maxfval,exitflag,output,lambda] = fminimax(varargin) maxfval = max(fval) end - endfunction |