A primal-dual splitting algorithm for monotone inclusions with applications
Abstract
In this paper, we study a broad class of structured monotone inclusion problems in real Hilbert spaces. We propose a novel primal-dual splitting algorithm for solving such inclusions, which accommodates multiple monotone operators and cocoercive terms, as well as a composite monotone operator involving the linear map. The algorithm combines forward evaluations for the cocoercive components with backward resolvent steps for the monotone operators and employs a dual update for the linear composition term. It generalizes and unifies several existing methods, while requiring only a single resolvent or operator evaluation per iteration. We prove weak convergence of the iterates under standard assumptions on monotonicity and cocoercivity. Furthermore, we establish strong convergence under a mild regularity condition, such as uniform monotonicity. Numerical experiments on image deblurring and denoising problems demonstrate the efficiency and flexibility of the proposed algorithm.
Versions
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BibTeX
@misc{huang2026primaldual,
title = {{A primal-dual splitting algorithm for monotone inclusions with applications}},
author = {Changchi Huang and Jigen Peng and Liqian Qin and Yuchao Tang},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2606.28010},
eprint = {2606.28010},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.28010},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A primal-dual splitting algorithm for monotone inclusions with applications
AU - Changchi Huang
AU - Jigen Peng
AU - Liqian Qin
AU - Yuchao Tang
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2606.28010
UR - https://arxiv.org/abs/2606.28010
AB - In this paper, we study a broad class of structured monotone inclusion problems in real Hilbert spaces. We propose a novel primal-dual splitting algorithm for solving such inclusions, which accommodates multiple monotone operators and cocoercive terms, as well as a composite monotone operator involving the linear map. The algorithm combines forward evaluations for the cocoercive components with backward resolvent steps for the monotone operators and employs a dual update for the linear composition term. It generalizes and unifies several existing methods, while requiring only a single resolvent or operator evaluation per iteration. We prove weak convergence of the iterates under standard assumptions on monotonicity and cocoercivity. Furthermore, we establish strong convergence under a mild regularity condition, such as uniform monotonicity. Numerical experiments on image deblurring and denoising problems demonstrate the efficiency and flexibility of the proposed algorithm.
ER -