An inertial forward–backward algorithm for the minimization of the sum of two nonconvex functions

We propose a forward–backward proximal-type algorithm with inertial/memory effects for minimizing the sum of a nonsmooth function with a smooth one in the nonconvex setting. Every sequence of iterates generated by the algorithm converges to a critical point of the objective function provided an appr...

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Autores principales:	Radu Ioan Boţ, Ernö Robert Csetnek, Szilárd Csaba László
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2016
Materias:	90C26 90C30 65K10 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/c2b91391253b4ec88bc07e3edc72bbe7
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spelling	oai:doaj.org-article:c2b91391253b4ec88bc07e3edc72bbe72021-12-02T05:00:47ZAn inertial forward–backward algorithm for the minimization of the sum of two nonconvex functions2192-440610.1007/s13675-015-0045-8https://doaj.org/article/c2b91391253b4ec88bc07e3edc72bbe72016-02-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2192440621000526https://doaj.org/toc/2192-4406We propose a forward–backward proximal-type algorithm with inertial/memory effects for minimizing the sum of a nonsmooth function with a smooth one in the nonconvex setting. Every sequence of iterates generated by the algorithm converges to a critical point of the objective function provided an appropriate regularization of the objective satisfies the Kurdyka-Łojasiewicz inequality, which is for instance fulfilled for semi-algebraic functions. We illustrate the theoretical results by considering two numerical experiments: the first one concerns the ability of recovering the local optimal solutions of nonconvex optimization problems, while the second one refers to the restoration of a noisy blurred image.Radu Ioan BoţErnö Robert CsetnekSzilárd Csaba LászlóElsevierarticle90C2690C3065K10Applied mathematics. Quantitative methodsT57-57.97Electronic computers. Computer scienceQA75.5-76.95ENEURO Journal on Computational Optimization, Vol 4, Iss 1, Pp 3-25 (2016)
institution	DOAJ
collection	DOAJ
language	EN
topic	90C26 90C30 65K10 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
spellingShingle	90C26 90C30 65K10 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95 Radu Ioan Boţ Ernö Robert Csetnek Szilárd Csaba László An inertial forward–backward algorithm for the minimization of the sum of two nonconvex functions
description	We propose a forward–backward proximal-type algorithm with inertial/memory effects for minimizing the sum of a nonsmooth function with a smooth one in the nonconvex setting. Every sequence of iterates generated by the algorithm converges to a critical point of the objective function provided an appropriate regularization of the objective satisfies the Kurdyka-Łojasiewicz inequality, which is for instance fulfilled for semi-algebraic functions. We illustrate the theoretical results by considering two numerical experiments: the first one concerns the ability of recovering the local optimal solutions of nonconvex optimization problems, while the second one refers to the restoration of a noisy blurred image.
format	article
author	Radu Ioan Boţ Ernö Robert Csetnek Szilárd Csaba László
author_facet	Radu Ioan Boţ Ernö Robert Csetnek Szilárd Csaba László
author_sort	Radu Ioan Boţ
title	An inertial forward–backward algorithm for the minimization of the sum of two nonconvex functions
title_short	An inertial forward–backward algorithm for the minimization of the sum of two nonconvex functions
title_full	An inertial forward–backward algorithm for the minimization of the sum of two nonconvex functions
title_fullStr	An inertial forward–backward algorithm for the minimization of the sum of two nonconvex functions
title_full_unstemmed	An inertial forward–backward algorithm for the minimization of the sum of two nonconvex functions
title_sort	inertial forward–backward algorithm for the minimization of the sum of two nonconvex functions
publisher	Elsevier
publishDate	2016
url	https://doaj.org/article/c2b91391253b4ec88bc07e3edc72bbe7
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An inertial forward–backward algorithm for the minimization of the sum of two nonconvex functions

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