Why do I get error if I try to minimize a function of the form x’Ay where A is data matrix and x and y are some variable that I want to minimize. The actual code has many other function in minimization and many constraints. I ma just giving the function where I get complain. The complain is:
Error using cvx/quad_form (line 230)
The second argument must be positive or negative semidefinite.
Error in * (line 261)
[ z2, success ] = quad_form( xx, P, Q, R );
Consider the special case of 1 dimension. Then your function is a*x*y . This is neither convex nor concave as a function of x and y, unless a = 0. You can see that by evaluating its Hessian. Things don’t get any better as the dimension is increased.
The expression x’Ay can be expressed as (sum over k ) c_k x1^a1kx2^a2k…
For example [x1,x2][C1 C2;C3 C4]*[x3 x4]=C1x1x3+C3x2x3+C32x1x4+C4x2x4 . Here as you see one can express the function in posynomial form with a’s are either 0 or 1. Since I can write the x’Ay as posynomial form why I cannot convert it to convex form. Please help.