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

Chinedu Izuchukwu (), Timilehin Opeyemi Alakoya (), Salissou Moutari () and Shengda Zeng ()
Additional contact information
Chinedu Izuchukwu: University of the Witwatersrand
Timilehin Opeyemi Alakoya: Queen’s University Belfast
Salissou Moutari: Queen’s University Belfast
Shengda Zeng: Yulin Normal University

Journal of Optimization Theory and Applications, 2025, vol. 207, issue 2, No 4, 33 pages

Abstract: Abstract 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 $$\mathcal {O}(\log (i)/(i))$$ 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.

Keywords: Reflected-forward-backward algorithm; Stochastic optimization; Inertial method; Monotone inclusion; Traffic flow network; 58E35; 47N10; 49J53; 90C25; 90C33 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-025-02779-1 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:207:y:2025:i:2:d:10.1007_s10957-025-02779-1

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-025-02779-1

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().