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<p>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 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10957_2025_2779_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="93" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {O}(\log (i)/(i))\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">O</mi> <mo stretchy="false">(</mo> <mo>log</mo> <mo stretchy="false">(</mo> <mi>i</mi> <mo stretchy="false">)</mo> <mo stretchy="false">/</mo> <mo stretchy="false">(</mo> <mi>i</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> 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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年7月21日

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  • Chinedu Izuchukwu,
  • Timilehin Opeyemi Alakoya,
  • Salissou Moutari,
  • Shengda Zeng

摘要

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.