Possible CVX solver for my convex problem


(Tran Khoa) #1

Dear,

I’ve been reading cvx userguide. Unfortunately, I’m unable to solve my current problem.

Is there any way to express the following convex problem such that it can be solved using cvx?

maximize
x(2)(log(1+5x(1)/x(2)) - log(1+3*x(1)/x(2))) subject to x(1)+x(2) <= 1, 0 <= x(1), x(2) <= 1.

the objective function is concave (i.e…, it is the perspective function of the concave function log(1+5x(1)) - log(1+3x(1))).

Thanks very much.

Cheers.


(Mark L. Stone) #2

I don’t think so. Your objective function may be concave over the constraint region you have provided, but it is not concave everywhere. For example, it is convex at x(1)=x(2) = -1. This is usually problematic for CVX.

With just the first term, you could use rel_entr, as in Writing a constraint in DCP complient format , but this can not be done with your 2 terms… Also see $\log(\frac{1+x\ (a+1)}{1+x \ a})$ and its perspective $y\log(\frac{1+x/y\ (a+1)}{1+x/y \ a})$ in CVX