Non-Submodular Maximization with Matroid and Knapsack Constraints

We investigate the problem of maximizing a gamma-submodular function subject to one or multiple matroid constraints and one knapsack constraint. By the greedy local search technique, we present approximation algorithms with constant approximation ratios. When gamma = 1, our model reduces to the regular submodular maximization problem investigated in the literature under the same type of constraints. Our results therefore contribute towards the line of research on constrained non-submodular function maximization.