MATLAB: Do I get the following error using fmincon

fminconoptimization

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?

Best Answer

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 =
     []
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