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

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...

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Veröffentlicht in:Journal of global optimization Jg. 83; H. 4; S. 727 - 751
Hauptverfasser: Lu, Cheng, Yang, Wenguo, Yang, Ruiqi, Gao, Suixiang
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.08.2022
Springer
Springer Nature B.V
Schlagworte:
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
ISSN:0925-5001, 1573-2916
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Zusammenfassung: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 )-approximate solution. To the best of our knowledge, it’s the first algorithm achieving the tight approximation guarantee for such maximization problem. In addition, we study the maximization of the sum of submodular and supermodular functions. We show that this problem can be reduced to the maximization of submodular and linear sums. Based on this reduction, we derive new and improved approximation bounds for the problem under various types of constraints.
Bibliographie:ObjectType-Article-1
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-021-01123-x