How to write the concave expression in CVX?

1

Hello, I have a expression, which i have checked to be a concave function. the expression is r_{k}= \tau \log_{2}[1+c*\sum_{k=1}^{K}(\frac{f_{k}}{\tau})], where c is a constant number, and \tau and f_{k} are variables. How to write this expression in cvx, if my optimization problem is max r_{k}. Kindly give the guidance. Thank you.

2

x*log(1+y/x) can be formulated as -rel_entr(x,x+y)

So If I am correctly reading your expression, I think your expression would be
-rel_entr(tau,tau+c*sum(f))/log(2)

Please check the correctness in case I misread your expression.

1 Like
3

Thank you. Yes the expression is correct. I will try with this and let you know.