A generalized forward-backward splitting operator: Degenerate analysis and applications
Optimization and Control
2023-02-21 v2
Abstract
In this paper, we study the nonexpansive properties of a generalized forward-backward splitting (G-FBS) operator, particularly under the setting of degenerate metric, from which follow the convergence results in terms of degenerate metric of the associated fixed-point iterations. The descent lemma and sufficient decrease property are also extended to degenerate case. It is further shown that the G-FBS operator provides a simplifying and unifying framework to model and analyze a great variety of operator splitting algorithms, many existing results are exactly recovered or relaxed from our general results.
Cite
@article{arxiv.2109.02064,
title = {A generalized forward-backward splitting operator: Degenerate analysis and applications},
author = {Feng Xue},
journal= {arXiv preprint arXiv:2109.02064},
year = {2023}
}
Comments
31 pages. published in Computational and Applied Mathematics, 2023. arXiv admin note: text overlap with arXiv:2108.06502