On the rate of convergence of the proximal alternating linearized minimization algorithm for convex problems

We analyze the proximal alternating linearized minimization algorithm (PALM) for solving non-smooth convex minimization problems where the objective function is a sum of a smooth convex function and block separable non-smooth extended real-valued convex functions. We prove a global non-asymptotic su...

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Autores principales:	Ron Shefi, Marc Teboulle
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2016
Materias:	90C25 49M27 65K05 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/24f455963618473180d6a3a1fc22c476
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spelling	oai:doaj.org-article:24f455963618473180d6a3a1fc22c4762021-12-02T05:00:48ZOn the rate of convergence of the proximal alternating linearized minimization algorithm for convex problems2192-440610.1007/s13675-015-0048-5https://doaj.org/article/24f455963618473180d6a3a1fc22c4762016-02-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2192440621000538https://doaj.org/toc/2192-4406We analyze the proximal alternating linearized minimization algorithm (PALM) for solving non-smooth convex minimization problems where the objective function is a sum of a smooth convex function and block separable non-smooth extended real-valued convex functions. We prove a global non-asymptotic sublinear rate of convergence for PALM. When the number of blocks is two, and the smooth coupling function is quadratic we present a fast version of PALM which is proven to share a global sublinear rate efficiency estimate improved by a squared root factor. Some numerical examples illustrate the potential benefits of the proposed schemes.Ron ShefiMarc TeboulleElsevierarticle90C2549M2765K05Applied mathematics. Quantitative methodsT57-57.97Electronic computers. Computer scienceQA75.5-76.95ENEURO Journal on Computational Optimization, Vol 4, Iss 1, Pp 27-46 (2016)
institution	DOAJ
collection	DOAJ
language	EN
topic	90C25 49M27 65K05 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
spellingShingle	90C25 49M27 65K05 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95 Ron Shefi Marc Teboulle On the rate of convergence of the proximal alternating linearized minimization algorithm for convex problems
description	We analyze the proximal alternating linearized minimization algorithm (PALM) for solving non-smooth convex minimization problems where the objective function is a sum of a smooth convex function and block separable non-smooth extended real-valued convex functions. We prove a global non-asymptotic sublinear rate of convergence for PALM. When the number of blocks is two, and the smooth coupling function is quadratic we present a fast version of PALM which is proven to share a global sublinear rate efficiency estimate improved by a squared root factor. Some numerical examples illustrate the potential benefits of the proposed schemes.
format	article
author	Ron Shefi Marc Teboulle
author_facet	Ron Shefi Marc Teboulle
author_sort	Ron Shefi
title	On the rate of convergence of the proximal alternating linearized minimization algorithm for convex problems
title_short	On the rate of convergence of the proximal alternating linearized minimization algorithm for convex problems
title_full	On the rate of convergence of the proximal alternating linearized minimization algorithm for convex problems
title_fullStr	On the rate of convergence of the proximal alternating linearized minimization algorithm for convex problems
title_full_unstemmed	On the rate of convergence of the proximal alternating linearized minimization algorithm for convex problems
title_sort	on the rate of convergence of the proximal alternating linearized minimization algorithm for convex problems
publisher	Elsevier
publishDate	2016
url	https://doaj.org/article/24f455963618473180d6a3a1fc22c476
work_keys_str_mv	AT ronshefi ontherateofconvergenceoftheproximalalternatinglinearizedminimizationalgorithmforconvexproblems AT marcteboulle ontherateofconvergenceoftheproximalalternatinglinearizedminimizationalgorithmforconvexproblems
_version_	1718400817888755712

On the rate of convergence of the proximal alternating linearized minimization algorithm for convex problems

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