# How to implement the pointwise infimum of a set of concave functions in CVX?

I met a problem about implementing the pointwise infimum of a set of concave functions in CVX, and I do not know how to deal with it, so I turn to you for help.

I have a function which is given by

y§ = inf{f(v) + s§/v + (a - 1/v)*h§ | v >= b}

where both a and b are constant parameters and a >= 1/b (note that b > 0). Besides, f(), s(), and h() are concave functions.

Hence, for each v >= b, f(v) + s§/v + (a - 1/v)*h§ is concave. As a result, y§ is the pointwise infimum of a set of concave functions and thus, it is a concave function from convex analysis.

However, f(v) + s§/v + (a - 1/v)*h§ is not jointly convex in (v,p). More specifically, given a p, f(v) + s§/v + (a - 1/v)*h§ is not a convex expression, or to say, it does not conform to the DCP ruleset.

Anyway, y§ is concave function in p. I do not know how to implement it in CVX, please help me. Thank you very much.

It cannot be done, I am afraid. The list of supported functions in CVX is exhaustive. If you cannot express your problem in terms of those functions, combined according to the disciplined convex programming rules, then CVX cannot support it.