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

arXiv: https://arxiv.org/abs/2109.02064 · HTML: https://mlsanity.com/paper/2109.02064/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Sep 2021.

## Built on by (most cited first, 1 of 1)

- [HPPP: Halpern-type Preconditioned Proximal Point Algorithms and Applications to Image Restoration](https://mlsanity.com/paper/2407.13120/) (2024)

## Abstract (arXiv)

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.