Projective Splitting as a Warped Proximal Algorithm

TL;DR

This paper demonstrates that the asynchronous block-iterative primal-dual projective splitting framework can be interpreted as a specific case of the recently developed warped proximal algorithm, providing new insights into its structure.

Contribution

It establishes a connection between the primal-dual splitting framework and warped proximal algorithms, offering a novel perspective on their relationship.

Findings

Unified view of splitting and warped proximal methods

Potential for improved algorithmic design and analysis

Enhanced understanding of convergence properties

Abstract

We show that the asynchronous block-iterative primal-dual projective splitting framework introduced by P. L. Combettes and J. Eckstein in their 2018 Math. Program. paper can be viewed as an instantiation of the recently proposed warped proximal algorithm.