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## Understanding the syntax of the minimax constraint problem

Asked by Clarisha Nijman

### Clarisha Nijman (view profile)

on 29 Nov 2018
Latest activity Commented on by Clarisha Nijman

### Clarisha Nijman (view profile)

on 30 Nov 2018
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

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## 1 Answer

Answer by Alan Weiss

### Alan Weiss (view profile)

on 29 Nov 2018

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

### Clarisha Nijman (view profile)

on 30 Nov 2018
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+x2^248x140x2+304,
f2(x)=x1^2−3x2^2,
f3(x)=x1+3x218,
f4(x)=x1x2,
f5(x)=x1+x28.
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,

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