A generalized forward-backward splitting operator: Degenerate analysis and applications

Feng Xue

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arXiv · 2109.02064

A generalized forward-backward splitting operator: Degenerate analysis and applications

Feng Xue

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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.

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Feng Xue. 2023-02-19. A generalized forward-backward splitting operator: Degenerate analysis and applications. https://arxiv.org/abs/2109.02064

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