## Framing a Combinatorial Optimization problem

I'm facing a combinatorial optimization problem whose name I don't know but I presume to be quite common. I would be very grateful for any hint at a name or pointer to the literature.

I want to minimize a function $f$ returning a scalar which takes as argument $M$ points from a set $\mathcal{S} = \lbrace x_1,...,x_N \rbrace$ where $M < N$. In other words, the problem consists in selecting the subset of $M$ points that minimize $f$.

-
A priori $f$ takes $2^N - 1$ unrelated values that you just have to look through to find the minimum. What else do you know about $f$? Is the containment order relevant at all? – Qiaochu Yuan Jun 10 at 4:59
I voted this down because it's not a reasonable question. Without some more information about the problem, we can't say anything more than "try all solutions". – Carl Feynman Jun 13 at 2:15