Parametrization and convergence of a primal-dual block-coordinate approach to linearly-constrained nonsmooth optimization

This note is concerned with the problem of minimizing a separable, convex, composite (smooth and nonsmooth) function subject to linear constraints. We study a randomized block-coordinate interpretation of the Chambolle-Pock primal-dual algorithm, based on inexact proximal gradient steps. A specifici...

Full description

Saved in:
Bibliographic Details
Main Author Bilenne, Olivier
Format Journal Article
LanguageEnglish
Published 29.08.2024
Subjects
Computer Science - Distributed, Parallel, and Cluster Computing
Computer Science - Multiagent Systems
Mathematics - Optimization and Control
Online AccessGet full text
DOI10.48550/arxiv.2408.16424

Cover

More Information
Summary:This note is concerned with the problem of minimizing a separable, convex, composite (smooth and nonsmooth) function subject to linear constraints. We study a randomized block-coordinate interpretation of the Chambolle-Pock primal-dual algorithm, based on inexact proximal gradient steps. A specificity of the considered algorithm is its robustness, as it converges even in the absence of strong duality or when the linear program is inconsistent. Using matrix preconditiong, we derive tight sublinear convergence rates with and without duality assumptions and for both the convex and the strongly convex settings. Our developments are extensions and particularizations of original algorithms proposed by Malitsky (2019) and Luke and Malitsky (2018). Numerical experiments are provided for an optimal transport problem of service pricing.
DOI:10.48550/arxiv.2408.16424