Inertial Stochastic Reflected Forward Backward Method with Applications to Traffic Network Problems

This paper introduces a new inertial stochastic reflected-forward-backward splitting method aimed at addressing monotone inclusion problems, specifically involving a maximal monotone set-valued operator and a single-valued Lipschitz continuous and monotone operator within a real separable Hilbert sp...

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Veröffentlicht in:Journal of optimization theory and applications Jg. 207; H. 2; S. 23
Hauptverfasser: Izuchukwu, Chinedu, Alakoya, Timilehin Opeyemi, Moutari, Salissou, Zeng, Shengda
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.11.2025
Springer Nature B.V
Schlagworte:
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Convergence
Engineering
Hilbert space
Lipschitz condition
Machine learning
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Operators (mathematics)
Optimization
Random variables
Signal processing
Splitting
Theory of Computation
Traffic assignment
Traffic control
Traffic flow
58E35
Monotone inclusion
49J53
90C25
90C33
Inertial method
Stochastic optimization
Traffic flow network
47N10
Reflected-forward-backward algorithm
ISSN:0022-3239, 1573-2878
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Zusammenfassung:This paper introduces a new inertial stochastic reflected-forward-backward splitting method aimed at addressing monotone inclusion problems, specifically involving a maximal monotone set-valued operator and a single-valued Lipschitz continuous and monotone operator within a real separable Hilbert space. Distinct from many existing inertial splitting approaches, this algorithm uniquely depends on one unbiased estimate of the monotone Lipschitz continuous operator and a single backward computation of the maximal monotone operator per iteration. We establish a convergence rate of O ( log ( i ) / ( i ) ) in expectation for a case of strong monotonicity, and almost sure convergence for a general monotone scenario. Furthermore, we examine its application to traffic flow networks.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-025-02779-1