Block-coordinate primal-dual method for the nonsmooth minimization over linear constraints

We consider the problem of minimizing a convex, separable, nonsmooth function subject to linear constraints. The numerical method we propose is a block-coordinate extension of the Chambolle-Pock primal-dual algorithm. We prove convergence of the method without resorting to assumptions like smoothnes...

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Bibliographic Details
Published inarXiv.org
Main Authors D Russell Luke, Malitsky, Yura
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 15.01.2018
Subjects
Algorithms
Convergence
Convexity
Mathematical analysis
Mathematics - Optimization and Control
Matrix methods
Numerical methods
Smoothness
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ISSN2331-8422
DOI10.48550/arxiv.1801.04782

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Summary:We consider the problem of minimizing a convex, separable, nonsmooth function subject to linear constraints. The numerical method we propose is a block-coordinate extension of the Chambolle-Pock primal-dual algorithm. We prove convergence of the method without resorting to assumptions like smoothness or strong convexity of the objective, full-rank condition on the matrix, strong duality or even consistency of the linear system. Freedom from imposing the latter assumption permits convergence guarantees for misspecified or noisy systems.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.1801.04782