An approximation proximal gradient algorithm for nonconvex-linear minimax problems with nonconvex nonsmooth terms

Nonconvex minimax problems have attracted significant attention in machine learning, wireless communication and many other fields. In this paper, we propose an efficient approximation proximal gradient algorithm for solving a class of nonsmooth nonconvex-linear minimax problems with a nonconvex nons...

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Veröffentlicht in:Journal of global optimization Jg. 90; H. 1; S. 73 - 92
Hauptverfasser: He, Jiefei, Zhang, Huiling, Xu, Zi
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.09.2024
Springer
Springer Nature B.V
Schlagworte:
Algorithms
Approximation
Computer Science
Convex analysis
Convexity
Machine learning
Mathematics
Mathematics and Statistics
MIMO communications
Minimax technique
Operations Research/Decision Theory
Optimization
Real Functions
Wireless communications
Nonsmooth problem
Iteration complexity
90C30
90C47
90C26
Nonconvex-linear minimax problem
Approximation proximal gradient algorithm
ISSN:0925-5001, 1573-2916
Online-Zugang:Volltext
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Zusammenfassung:Nonconvex minimax problems have attracted significant attention in machine learning, wireless communication and many other fields. In this paper, we propose an efficient approximation proximal gradient algorithm for solving a class of nonsmooth nonconvex-linear minimax problems with a nonconvex nonsmooth term, and the number of iteration to find an ε -stationary point is upper bounded by O ( ε - 3 ) . Some numerical results on one-bit precoding problem in massive MIMO system and a distributed non-convex optimization problem demonstrate the effectiveness of the proposed algorithm.
Bibliographie:ObjectType-Article-1
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-024-01383-3