The optimization of shannon formula

(Qirui Liu) #1

the optimal function is shannon formula,xlog(1+y/x), but the" * " was not accepted by cvx, because :Cannot perform the operation: {log-affine} . {convex},why? I know the function is jointly concave W.R.T x and y.

(Mark L. Stone) #2

See mcg’s answer at Perspective function for the solution -rel_entr(x,x+y)

(Qirui Liu) #3

Thank you very much! I have been confused for a long time, and I’ve changed the objective function to -rel_entr(x,x+y). What I want to compute is the maximization of
xlog(1+y/x)-f(y), which the first part is concave and the second part is linear function, and the problem should be concave. However the cvx showed error: said the problem is convex, and can not be maximized… why? Do please help me, thank you!

(Mark L. Stone) #4

Please show a reproducible program, with error message. There must be something you’re not telling us, for instance that x or y are not affine, or some other aspect of your program.