How to write x*log(1+y) in cvx?

Nonconvex
1

How to write x*log(1+y) in cvx?

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2

Is that known to be a convex or concave function?

Also since convexity is dependent on how the term appears in the model there is no way we can answer that question.

You may want to take a look at

https://docs.mosek.com/cheatsheets/conic.pdf

btw.

3

Hi Erling,
Thank you for the reply. Yes, x*log(1+y) is concave jointly in x and y. I tried to formulate it using rel_entr and entr but could not do it. Can you help me here?

Best regards
Ashok

4

This in indefinite, i.e., neither convex nor concave. For instance, at x = y = 1, its Hessian has one positive eigenvalue and one negative eigenvalue. Therefore, this can not be handled by CVX.

5

bro, what about -(rel_entr(x, 1+y) + entr(x)) ?
i am not sure.

6

The first term is convex, the second one is concave. CVX won’t accept their sum because of DCP rule.

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