How to express x*log_2(a+b*y/x) in CVX manner?

1

Dear expert,
Thanks for your time. I want to consult a question.
How to express xlog_2(a+by/x) in the CVX manner? x and y are variables, a and b are constants, so xlog_2(a+by/x) is a concave function.

2

As has been used on this forum many times,
x*log(1+y/x) = -rel_entr(x,x+y)

Converting to this “standard” form,

x*log2(a+b*y/x) = (-rel_entr(x,x+b/a*y)+log(a)*x)/log(2)

3

Thanks for your patience and time. This will help me a lot.