An inexact inertial projective splitting algorithm with strong convergence

Fuente: arXiv
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Main Authors: Alves, M. Marques, Caballero, J. E. Navarro, Marcavillaca, R. T.
Format: Preprint
Published: 2025
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author Alves, M. Marques
Caballero, J. E. Navarro
Marcavillaca, R. T.
author_facet Alves, M. Marques
Caballero, J. E. Navarro
Marcavillaca, R. T.
contents We propose and study a strongly convergent inexact inertial projective splitting (PS) algorithm for finding zeros of composite monotone inclusion problems involving the sum of finitely many maximal monotone operators. Strong convergence of the iterates is ensured by projections onto the intersection of appropriately defined half-spaces, even in the absence of inertial effects. We also establish iteration-complexity results for the proposed PS method, which likewise hold without requiring inertial terms. The algorithm includes two inertial sequences, controlled by parameters satisfying mild conditions, while preserving strong convergence and enabling iteration-complexity analysis. Furthermore, for more structured monotone inclusion problems, we derive two variants of the main algorithm that employ forward-backward and forward-backward-forward steps.
format Preprint
id arxiv_https___arxiv_org_abs_2507_05382
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle An inexact inertial projective splitting algorithm with strong convergence
Alves, M. Marques
Caballero, J. E. Navarro
Marcavillaca, R. T.
Optimization and Control
We propose and study a strongly convergent inexact inertial projective splitting (PS) algorithm for finding zeros of composite monotone inclusion problems involving the sum of finitely many maximal monotone operators. Strong convergence of the iterates is ensured by projections onto the intersection of appropriately defined half-spaces, even in the absence of inertial effects. We also establish iteration-complexity results for the proposed PS method, which likewise hold without requiring inertial terms. The algorithm includes two inertial sequences, controlled by parameters satisfying mild conditions, while preserving strong convergence and enabling iteration-complexity analysis. Furthermore, for more structured monotone inclusion problems, we derive two variants of the main algorithm that employ forward-backward and forward-backward-forward steps.
title An inexact inertial projective splitting algorithm with strong convergence
topic Optimization and Control
url https://arxiv.org/abs/2507.05382