There is an
x*y term, which is indefinite, hence not concave, which the argument of log must be to be accepted by CVX.
This is not just a matter of CVX not realizing it's concave. It is NOT concave. For example, let
a1 = 1, a2 = -1, a3 = 1, x= -1, y = -2. Then the eigenvalues of the Hessian are -1/ln(2) and 1/ln(2), hence indefinite. Yes, it's true that it is concave at some values of x and y, but that's not good enough.