Given an undirected graph $G = (V, E)$ and a function $f: 2^V \to \mathbb{R}^+,$ where $2^V$ is the set of all subsets of $V$. Find a connected subgraph $T = (V_T, E_T)$ of k vertices such that $f(V_T)$ is maximum.
This problem is a generalization of the maximum connected subgraph of size $k$, which can be solved by means of integer linear programming. Unfortunately, my objective function $f$ is nonlinear. One can enumerate all connected subgraphs of size $k$ and take one with the largest objective value. However, I think this approach is very slow. I also tried the color-coding technique but it is slow too. Does anyone know any best/fast algorithms to solve this problem in a such general scheme? Thank you in advance!