Understanding the syntax of the minimax constraint problem

Dear all I am trying to solve a minimax constraint problem, where the objective function is an absolute function.

Given the data set A with 3 variables,x(1), x(2) and x(3) and an unknown error term x(4):

0.0027 0.0025 0.0025

0.0028 0.0030 0.0029

0.0030 0.0031 0.0031

0.0031 0.0031 0.0032

0.0032 0.0032 0.0033

0.0033 0.0033 0.0034

0.0035 0.0035 0.0035

0.0036 0.0032 0.0036

0.0031 0.0037 0.0037

I define the absolute function of the minimax problem:

function F = maximizefunc(A)

for i=1:size(A,1)

F(i)=A(i,1)*x(1)+A(i,2)*x(2)+A(i,3)*x(3)+x(4);

end

end

% Make a starting guess at solution

x0 = 0.1*rand(4,1);

and apply the code given in on of the last examples on the matlab site (https://nl.mathworks.com/help/optim/ug/fminimax.html)

options = optimoptions('fminimax','AbsoluteMaxObjectiveCount',5); % Minimize abs. values

[x,fval] = fminimax(@maximizefunc,x0,...

[],[],[],[],[],[],[],options);

But I am getting only errors saying:

Function definitions in a script must appear at the end of the file.

Move all statements after the "maximizefunc" function definition to before the function definition.

Error in fminimax (line 351)

user_f = feval(funfcn{3},x,varargin{:});

Does anyone have a suggestion for me? I do not really understand how the option function should be constructed. Can somebody give me some feedback pls.

Thank u in advance

Answer 1

[Alan Weiss]

Your problem is that you want to include a data matrix A as extra data, but you are doing it incorrectly. See Passing Extra Parameters. Your function should look like this:

function F = maximizefunc(x,A)
% code here
end

Then you call it like this:

[args] = fminimax(@(x)maximizefunc(x,A),[more args])

Alan Weiss

MATLAB mathematical toolbox documentation

[Clarisha Nijman]

Would I get the same result as in example below? (https://nl.mathworks.com/help/optim/ug/fminimax.html).

Find values of x that minimize the maximum value of

[f1(x), f2(x), f3(x), f4(x), f5(x)]

where

f1(x)=2x1^2+x2^2−48x1−40x2+304,

f2(x)=−x1^2−3x2^2,

f3(x)=x1+3x2−18,

f4(x)=−x1−x2,

f5(x)=x1+x2−8.

First, write a file that computes the five functions at x.

function f = myfun(x)

f(1)= 2*x(1)^2+x(2)^2-48*x(1)-40*x(2)+304; % Objectives

f(2)= -x(1)^2 - 3*x(2)^2;

f(3)= x(1) + 3*x(2) -18;

f(4)= -x(1)- x(2);

f(5)= x(1) + x(2) - 8;

Next, invoke an optimization routine.

x0 = [0.1; 0.1]; % Make a starting guess at solution

[x,fval] = fminimax(@myfun,x0);

The only difference is that my objective function is an absolute fucntion, so I combine the next instruction on that same wegpage with more instructions above.

instructions:

You can solve problems of the form

min x max i |Fi(x)|

by using the AbsoluteMaxObjectiveCount option; see Notes.

The information needed for the set of F functions can be retrieved from the given data set A,