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

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  • Chinedu Izuchukwu

    (University of the Witwatersrand)

  • Timilehin Opeyemi Alakoya

    (Queen’s University Belfast)

  • Salissou Moutari

    (Queen’s University Belfast)

  • Shengda Zeng

    (Yulin Normal University)

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.

Suggested Citation

  • Chinedu Izuchukwu & Timilehin Opeyemi Alakoya & Salissou Moutari & Shengda Zeng, 2025. "Inertial Stochastic Reflected Forward Backward Method with Applications to Traffic Network Problems," Journal of Optimization Theory and Applications, Springer, vol. 207(2), pages 1-33, November.
    • Handle: RePEc:spr:joptap:v:207:y:2025:i:2:d:10.1007_s10957-025-02779-1
    DOI: 10.1007/s10957-025-02779-1
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    References listed on IDEAS

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    1. Shisheng Cui & Uday Shanbhag & Mathias Staudigl & Phan Vuong, 2022. "Stochastic relaxed inertial forward-backward-forward splitting for monotone inclusions in Hilbert spaces," Computational Optimization and Applications, Springer, vol. 83(2), pages 465-524, November.
    2. Shengda Zeng & Nikolaos S. Papageorgiou & Patrick Winkert, 2023. "Inverse Problems for Double-Phase Obstacle Problems with Variable Exponents," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 666-699, February.
    3. Bing Tan & Xiaolong Qin & Jen-Chih Yao, 2022. "Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems," Journal of Global Optimization, Springer, vol. 82(3), pages 523-557, March.
    4. Ahmet Alacaoglu & Yura Malitsky & Volkan Cevher, 2021. "Forward-reflected-backward method with variance reduction," Computational Optimization and Applications, Springer, vol. 80(2), pages 321-346, November.
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