Invalid quadratic form: convex portion

Nonconvex
1

Hi,

I have the toy example below. As expected CVX complains about x*y being an invalid quadratic form. Since my variables are positive, I am actually using convex portion of x*y. Is there a way to tell that to CVX?

Thanks.

cvx_begin
    variable x
    variable y

    minimize 5*x + 6*y + x*y
    subject to
    0<=x<=1
    0<=y<=1
cvx_end
2

x*y is not convex anywhere, and neither is your overall objective function. Its Hessian (and that of your overall objective function) is a constant, and is [0 1;1 0], which has eigenvalues of -1 and 1, and so is indefinite.