Near-Optimal Solution of Generalized Resource Allocation Problems with Large Capacities

We consider problems of allocating resources to activities where the allocation to each activity is restricted to a general set of admissible values, the objective function is additively-separable but not necessarily concave nor differentiable, and each activity uses at most one resource. We develop a simple algorithm, based on a nonsmooth convex relaxation, that generates a near-optimal solution whenever each allocation is a small fraction of resource capacity.