In this paper, we present a forward–backward linesearch–based algorithm suited for the minimization of the sum of a smooth (possibly nonconvex) function and a convex (possibly nonsmooth) term. Such algorithm first computes inexactly the proximal operator with respect to a given Bregman distance, and then ensures a sufficient decrease condition by performing a linesearch along the descent direction. The proposed approach can be seen as an instance of the more general class of descent methods presented in [1], however, unlike in [1], we do not assume the strong convexity of the Bregman distance used in the proximal evaluation. We prove that each limit point of the iterates sequence is stationary, we show how to compute an approximate proximal–gradient point with respect to a Bregman distance and, finally, we report the good numerical performance of the algorithm on a large scale image restoration problem. [1] S. Bonettini, I. Loris, F. Porta, and M. Prato 2016, Variable metric inexact line-search-based methods for nonsmooth optimization, SIAM J. Optim. 26(2), 891–921.

A Bregman inexact linesearch-based forward-backward algorithm for nonsmooth nonconvex optimization / Rebegoldi, S.; Bonettini, S.; Prato, M.. - In: JOURNAL OF PHYSICS. CONFERENCE SERIES. - ISSN 1742-6588. - 1131:(2018). ((Intervento presentato al convegno 8th International Conference on New Computational Methods for Inverse Problems tenutosi a Cachan nel 25 maggio 2018 [10.1088/1742-6596/1131/1/012013].

A Bregman inexact linesearch-based forward-backward algorithm for nonsmooth nonconvex optimization

S. Rebegoldi
;
S. Bonettini;M. Prato
2018

Abstract

In this paper, we present a forward–backward linesearch–based algorithm suited for the minimization of the sum of a smooth (possibly nonconvex) function and a convex (possibly nonsmooth) term. Such algorithm first computes inexactly the proximal operator with respect to a given Bregman distance, and then ensures a sufficient decrease condition by performing a linesearch along the descent direction. The proposed approach can be seen as an instance of the more general class of descent methods presented in [1], however, unlike in [1], we do not assume the strong convexity of the Bregman distance used in the proximal evaluation. We prove that each limit point of the iterates sequence is stationary, we show how to compute an approximate proximal–gradient point with respect to a Bregman distance and, finally, we report the good numerical performance of the algorithm on a large scale image restoration problem. [1] S. Bonettini, I. Loris, F. Porta, and M. Prato 2016, Variable metric inexact line-search-based methods for nonsmooth optimization, SIAM J. Optim. 26(2), 891–921.
8th International Conference on New Computational Methods for Inverse Problems
Cachan
25 maggio 2018
1131
Rebegoldi, S.; Bonettini, S.; Prato, M.
A Bregman inexact linesearch-based forward-backward algorithm for nonsmooth nonconvex optimization / Rebegoldi, S.; Bonettini, S.; Prato, M.. - In: JOURNAL OF PHYSICS. CONFERENCE SERIES. - ISSN 1742-6588. - 1131:(2018). ((Intervento presentato al convegno 8th International Conference on New Computational Methods for Inverse Problems tenutosi a Cachan nel 25 maggio 2018 [10.1088/1742-6596/1131/1/012013].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11380/1160199
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