CODEWITHSUNDEEP
matlab
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Reputation: 2299

fmincon in Matlab with non scalar objective function

I want to use Matlab to solve a constrained minimisation problem:

min wrto (gamma,delta) the function f(gamma,delta):=[gamma,delta]

such that

A(gamma,delta)-B(gamma,delta)<=0

Here a working example:

%main file
gamma0=0.4;
delta0=0.5;
x=fmincon(@(x) [x(1) x(2)], [gamma0 delta0], ...
          [],[],[],[],[],[], ...
          @(x) mycon(x(1),x(2))); 


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%function for constraints
function [C,Ceq]=mycon(gamma,delta)
    A=randn(1)+gamma+delta;
    B=randn(1)+gamma+delta;
    C=A-B;
    Ceq=[];
end

However, I get as error 

Error using fmincon (line 607)
User supplied objective function must return a scalar value.

Could you help me to understand how to modify the code so that fmincon accepts also the desired non-scalar output function?

Upvotes: 1

Views: 416

Answers (1)

m7913d
m7913d

Reputation: 11072

Calculating the minimum of a non scalar objective function is mathematically not defined. As an alternative, you can minimise one of the following options:

  • x(1) or x(2) alone
  • a weighted combination of both (typically L1, L2 or L_infinity norm)

Other considerations

  • Variables that are not part of the objective function may change in order to minimise the other variables further if they are part of the constraint function.

  • Using a random generator such as randn inside the objective/constraint function is (often) a bad idea, because fmincon calls them multiple times for different input arguments resulting in a randomly changing objective/constraint function. You should generate the random variables before the call to fmincon as pass these variables as arguments to your functions.

Upvotes: 1

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