Fast deterministic algorithms for non-submodular maximization with strong performance guarantees

We study the non-submodular maximization problem, in which the objective function is characterized by parameters, subject to a cardinality or p -system constraint. By adapting the Threshold-Greedy algorithm for the submodular maximization, we present two deterministic algorithms for approximately so...

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Bibliographic Details
Published in:Journal of global optimization Vol. 89; no. 3; pp. 777 - 801
Main Authors: Lu, Cheng, Yang, Wenguo
Format: Journal Article
Language:English
Published: New York Springer US 01.07.2024
Springer
Springer Nature B.V
Subjects:
Algorithms
Analysis
Approximation
Computer Science
Greedy algorithms
Mathematics
Mathematics and Statistics
Maximization
Operations Research/Decision Theory
Optimization
Real Functions
Greedy algorithm
Non-submodular maximization
Independence system
Curvature
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:We study the non-submodular maximization problem, in which the objective function is characterized by parameters, subject to a cardinality or p -system constraint. By adapting the Threshold-Greedy algorithm for the submodular maximization, we present two deterministic algorithms for approximately solving the non-submodular maximization problem. Our analysis shows that the algorithms we propose requires much less function evaluations than existing algorithms, while providing comparable approximation guarantees. Moreover, numerical experiment results are presented to validate the theoretical analysis. Our results not only fill a gap in the (non-)submodular maximization, but also generalize and improve several existing results on closely related optimization problems.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-024-01371-7