passing matrices in fmincon objective function

My objective function has matrices of below sizes

A = 150x50, B = 150x150

objective function is J = p*A'*B*A*p

Below is the code I am using -

p0 = 0.3;
plb = -0.5;
pup = 0.5;  

[p,cost] = fmincon(@(p) mycost(p),p0,[],[],[],[],plb,pup);

function J = mycost(p)
% created matrices A(150x50) & B(150x150)
J = (p*A'*B*A*p);
end

My objective function size with these matrices will be 50x50. I am trying to get value of p by minimizing the objective function. I am getting following error -

"Supplied objective function must return a scalar value."

Answer 1

[Alan Weiss]

What does it mean to minimize a function that has more than one dimension? The answer is, the problem is ill-defined, there is no one meaning to this question. fmincon minimizes only scalar-valued functions.

Maybe you mean to minimize the sum of squares of the entries in J. Maybe you mean to minimize the maximum entry. Maybe you mean to minimize the sum of absolute values of the entries. See, there is no unique meaning to minimizing a function with multiple outputs. No solver will do that.

If you mean to minimize the sum of squares of the entries, you can use lsqnonlin with a slight change in syntax.

Alan Weiss

MATLAB mathematical toolbox documentation