A problem of 'log' in objective function

I have a problem such as

minimize sum(S) - a * log2( 1 + S(1) / (S(2)+S(3)+N) ) - b * log2( 1 + S(2) / (S(1)+S(3)+N) ) - c * log2( 1 + S(3) / (S(1)+S(2)+N) )

where S is the variables to be optimized,
This problem is convex to S, how can I express this problem in CVX?

The problem description just now is not clear, sorry~

Thanks very much for your answer~ :slight_smile:

This is non-convex. If you have a proof otherwise, and are under the age of 40, you might get the Fields Medal.

Thank you very much~
I need to rethink it seriously :sob: