Maximizing a non-decreasing non-submodular function subject to various types of constraints

• Published in: Journal of global optimization Vol. 83; no. 4; pp. 727 - 751
• Main Authors: Lu, Cheng, Yang, Wenguo, Yang, Ruiqi, Gao, Suixiang
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.08.2022; Springer; Springer Nature B.V
• Subjects: Algorithms; Approximation; Computer Science; Design; Machine learning; Mathematical analysis; Mathematics; Mathematics and Statistics; Maximization; Operations Research/Decision Theory; Optimization; Real Functions; Search algorithms; Local search; Supermodular function; Non-submodular maximization; Weakly DR-submodular function; Curvature; Matroid

In this paper, we firstly study the problem of maximizing a γ -weakly DR-submodular function under a general matroid constraint. We present a local search algorithm, which is guided by a tailored potential function, for solving this problem. We prove that our algorithm produces a ( 1 - e - γ - ϵ )-a...