CVX rate LOG

1

Hey,
I’m trying to implement the following optimization problem:

          max                   a * log(1 + H11(hermitian) * X1 * H11)
X1 >= 0 , X2 >= 0 , Y >= 0
s.T.    H21(hermitian) * X2 * H22 + Y * sigma1.^2 = 1
H12(hermitian) * X1 * H12 + H22(hermitian) * X2 * H22 >= Y * E2/a
Tr(X1) <= y* P1 , Tr(X2) <= y* P2

with the following correspondence:

y = 1/(H21(hermitian) * S2 * H21 + sigma1.^2) > 0,
X1 = Y * S1 , X2 = Y * S2

Always getting an error due to the log. I dont really know how to solve this problem without the logarithm.

2

I strongly suspect this problem is not convex. Even if it is, it almost certainly cannot be solved by CVX. You should be able to drop the logarithm, but that still leaves the maximization of a convex objective.