Weak and strong convergence of a general splitting approach for monotone multioperator inclusions
Abstract
In this paper, we study a general forward-backward splitting approach for monotone inclusion problems that simultaneously accommodate set-valued, monotone Lipschitz continuous, and cocoercive operators. Weak convergence is established under a general setting. Strong convergence is obtained when both the maximally monotone operators are linear relations and the monotone Lipschitz continuous and cocoercive operators are linear. When the set-valued operators are normal cones to closed linear subspaces, we derive an explicit characterization of limit points of generated sequences using a new technique. Numerical experiments on a quadratic minimization problem with multiple-set split feasibility constraints are presented to illustrate the theoretical results.
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BibTeX
@misc{dao2026weak,
title = {{Weak and strong convergence of a general splitting approach for monotone multioperator inclusions}},
author = {Minh N. Dao and Matthew K. Tam and Thang D. Truong},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05884},
eprint = {2611.05884},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05884},
}
RIS
TY - UNPB
TI - Weak and strong convergence of a general splitting approach for monotone multioperator inclusions
AU - Minh N. Dao
AU - Matthew K. Tam
AU - Thang D. Truong
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.05884
UR - https://arxiv.org/abs/2611.05884
AB - In this paper, we study a general forward-backward splitting approach for monotone inclusion problems that simultaneously accommodate set-valued, monotone Lipschitz continuous, and cocoercive operators. Weak convergence is established under a general setting. Strong convergence is obtained when both the maximally monotone operators are linear relations and the monotone Lipschitz continuous and cocoercive operators are linear. When the set-valued operators are normal cones to closed linear subspaces, we derive an explicit characterization of limit points of generated sequences using a new technique. Numerical experiments on a quadratic minimization problem with multiple-set split feasibility constraints are presented to illustrate the theoretical results.
ER -