research-article

Preconditioned Douglas--Rachford Splitting Methods for Convex-concave Saddle-point Problems

Authors:

Kristian Bredies,

Hongpeng SunAuthors Info & Claims

SIAM Journal on Numerical Analysis, Volume 53, Issue 1

Pages 421 - 444

https://doi.org/10.1137/140965028

Published: 01 January 2015 Publication History

Abstract

We propose a preconditioned version of the Douglas--Rachford splitting method for solving convex-concave saddle-point problems associated with Fenchel--Rockafellar duality. Our approach makes it possible to use approximate solvers for the linear subproblem arising in this context. We prove weak convergence in Hilbert space under minimal assumptions. In particular, various efficient preconditioners are introduced in this framework for which only a few inner iterations are needed instead of computing an exact solution or controlling the error. The method is applied to a discrete total-variation denoising problem. Numerical experiments show that the proposed algorithms with appropriate preconditioners are very competitive with existing fast algorithms including the first-order primal-dual algorithm for saddle-point problems of Chambolle and Pock.

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Cited By

Zietlow CLindner J(2024)ADMM-TGV image restoration for scientific applications with unbiased parameter choiceNumerical Algorithms10.1007/s11075-024-01759-297:4(1481-1512)Online publication date: 1-Dec-2024
https://dl.acm.org/doi/10.1007/s11075-024-01759-2
Ding WNg MZhang W(2024)A generalized alternating direction implicit method for consensus optimization: application to distributed sparse logistic regressionJournal of Global Optimization10.1007/s10898-024-01418-990:3(727-753)Online publication date: 16-Jul-2024
https://dl.acm.org/doi/10.1007/s10898-024-01418-9
Zhang ZChang HDuan Y(2023)Fast Non-overlapping Domain Decomposition Methods for Continuous Multi-phase Labeling ProblemJournal of Scientific Computing10.1007/s10915-023-02382-497:3Online publication date: 2-Nov-2023
https://dl.acm.org/doi/10.1007/s10915-023-02382-4

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Published In

cover image SIAM Journal on Numerical Analysis

SIAM Journal on Numerical Analysis Volume 53, Issue 1

2015

633 pages

ISSN:0036-1429

DOI:10.1137/sjnaam.53.1

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© 2015, Society for Industrial and Applied Mathematics.

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 January 2015

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Cited By

Zietlow CLindner J(2024)ADMM-TGV image restoration for scientific applications with unbiased parameter choiceNumerical Algorithms10.1007/s11075-024-01759-297:4(1481-1512)Online publication date: 1-Dec-2024
https://dl.acm.org/doi/10.1007/s11075-024-01759-2
Ding WNg MZhang W(2024)A generalized alternating direction implicit method for consensus optimization: application to distributed sparse logistic regressionJournal of Global Optimization10.1007/s10898-024-01418-990:3(727-753)Online publication date: 16-Jul-2024
https://dl.acm.org/doi/10.1007/s10898-024-01418-9
Zhang ZChang HDuan Y(2023)Fast Non-overlapping Domain Decomposition Methods for Continuous Multi-phase Labeling ProblemJournal of Scientific Computing10.1007/s10915-023-02382-497:3Online publication date: 2-Nov-2023
https://dl.acm.org/doi/10.1007/s10915-023-02382-4

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