# Maximizing supermodular functions

I have a real supermodular objective function which I want to maximize with constraint. The constraint is on the size, like |A|=k .

I am wondering if anyone can give me more information about a practical solution applicable to a large set, particularly what we can say about the greedy algorithm?

There are several other approaches available for solving submodular minimization. Do not confuse it with submodular maximization (or supermodular minimization), for which there are greedy algorithms --- because these problems are NP-Hard to approximate to a factor better than $1-1/e$ unless more structure is assumed. Again, google will find you many hits on the greedy algorithm for submodular maximization.