Stochastic forward-backward-half forward splitting algorithm with variance reduction

In this paper, we present a stochastic forward-backward-half forward splitting algorithm with variance reduction for solving the structured monotone inclusion problem composed of a maximally monotone operator, a maximally monotone operator and a cocoercive operator in a separable real Hilbert space....

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Bibliographic Details
Published in:Optimization letters Vol. 19; no. 9; pp. 1997 - 2010
Main Authors: Qin, Liqian, Zhang, Yaxuan, Dong, Qiao-Li, Rassias, Michael Th
Format: Journal Article
Language:English
Published: Heidelberg Springer Nature B.V 01.12.2025
Subjects:
Algebra
Algorithms
Convergence
Euclidean space
Hilbert space
Liapunov functions
Operators (mathematics)
Random variables
Splitting
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ISSN:1862-4472, 1862-4480
Online Access:Get full text
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Summary:In this paper, we present a stochastic forward-backward-half forward splitting algorithm with variance reduction for solving the structured monotone inclusion problem composed of a maximally monotone operator, a maximally monotone operator and a cocoercive operator in a separable real Hilbert space. By defining a Lyapunov function, we establish the weak almost sure convergence of the proposed algorithm, and obtain the linear convergence when one of the maximally monotone operators is strongly monotone. Numerical examples are provided to show the performance of the proposed algorithm.
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ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-025-02201-9