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.