Why do I get the following error using fmincon?

I am trying to run the following fmincon problem, where evaluating fun requires to solve a linear programming problem.

Before showing you my code, let me write the optimisation problem in math symbols.

where x is a vector, is a vector of zeros, means that every element of x should be non-negative, are vectors of real numbers.

clear
rng default
XZW_temp=[0.5450    0.8175   -0.5451    0.2724]; %this is A1 above
X1_temp=[0    0.0852         0   -0.0852]; %this is A2 above
X2_temp=[2.0132    1.0066   -2.0132   -1.0066]; %this is A3 above
options = optimset('linprog');
options.Display = 'off';
 
fun=@(x)inner_max(x,XZW_temp, X1_temp, X2_temp, options);
ub=Inf*ones(4,1);
lb=zeros(4,1);
x0=ones(4,1);
[~, f]=fmincon(fun,x0,[],[],[],[],lb,ub); 

The function inner_max is

function i_m=inner_max(x,XZW_temp, X1_temp, X2_temp, options)
  f=-[x.'*XZW_temp.'; x.'*X1_temp.'; x.'*X2_temp.'];
  Aeq=[1 0 0];
  beq=1; 
  lb=-Inf*ones(3,1);
  ub=Inf*ones(3,1);
  [~,fval] = linprog(f,[],[],Aeq,beq,lb,ub,options);
  i_m=-fval; 
end

I get the following error

In an assignment  A(:) = B, the number of elements in A and B must be the same.
Error in finitedifferences
Error in computeFinDiffGradAndJac
Error in barrier
Error in fmincon (line 798)
    [X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] = barrier(funfcn,X,A,B,Aeq,Beq,l,u,confcn,options.HessFcn, ...

Could you help me to understand what is wrong?

[John D'Errico]

Notethat you do not need to make all bounds inf, if there are no bounds.

lb=-Inf*ones(3,1);
ub=Inf*ones(3,1);

Simpler and better is just:

lb = [];
ub = [];

[Matt J]

It would be better to rewrite this problem as a quadratic program and use quadprog. The objective to be minimized,

f(x,y)=-[x.'*XZW_temp.'; x.'*X1_temp.'; x.'*X2_temp.']*y;

is quadratic in (x,y) with all linear constraints on these variables.

[CT]

Thanks. How do you show that it reduces to one quadratic optimisation problem? It is a min-max problem. I have added the formulation of the problem at the beginning of my question.

[Matt J]

Never mind. You should be using fminimax, though.

[CT]

Thanks, but could not understand how to use fminimax in my case. In the examples the inner maximisation problem is always "discrete".

Answer 1

[Matt J]

Because the are unconstrained, the only way the inner max operation can have a finite result is if [A1;A2]*x=[0;0] and therefore the problem is equivalent to the linear program,

You can plug this into linprog

f=[0.5450    0.8175   -0.5451    0.2724]; %this is A1 above
A2=[0    0.0852         0   -0.0852]; %this is A2 above
A3=[2.0132    1.0066   -2.0132   -1.0066]; %this is A3 above


Aeq=[A2;A3]; beq=[0;0];
lb=zeros(4,1);

x=linprog(f,[],[],Aeq,beq,lb)

However, it finds that the problem is unbounded,

Problem is unbounded.

x =

     []

Answer 2

[Matt J]

Could you help me to understand what is wrong?

linprog() and therefore innermax() can return an empty matrix [] when it does not find a solution. Your code does not test for and provide a contingency for that situation.