We study a novel inertial proximal-gradient method for composite optimization. The proposed method alternates between a variablemetric proximal-gradient iterationwith momentum and an Armijo-like linesearch based on the sufficient decrease of a suitable merit function. The linesearch procedure allows for a major flexibility on the choice of the algorithm parameters. We prove the convergence of the iterates sequence towards a stationary point of the problem, in a Kurdyka–Łojasiewicz framework. Numerical experiments on a variety of convex and nonconvex problems highlight the superiority of our proposal with respect to several standard methods, especially when the inertial parameter is selected by mimicking the Conjugate Gradient updating rule.

A new proximal heavy ball inexact line-search algorithm / Bonettini, S.; Prato, M.; Rebegoldi, S.. - In: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS. - ISSN 0926-6003. - 88:2(2024), pp. 525-565. [10.1007/s10589-024-00565-9]

A new proximal heavy ball inexact line-search algorithm

Bonettini S.;Prato M.;Rebegoldi S.
2024

Abstract

We study a novel inertial proximal-gradient method for composite optimization. The proposed method alternates between a variablemetric proximal-gradient iterationwith momentum and an Armijo-like linesearch based on the sufficient decrease of a suitable merit function. The linesearch procedure allows for a major flexibility on the choice of the algorithm parameters. We prove the convergence of the iterates sequence towards a stationary point of the problem, in a Kurdyka–Łojasiewicz framework. Numerical experiments on a variety of convex and nonconvex problems highlight the superiority of our proposal with respect to several standard methods, especially when the inertial parameter is selected by mimicking the Conjugate Gradient updating rule.
2024
88
2
525
565
A new proximal heavy ball inexact line-search algorithm / Bonettini, S.; Prato, M.; Rebegoldi, S.. - In: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS. - ISSN 0926-6003. - 88:2(2024), pp. 525-565. [10.1007/s10589-024-00565-9]
Bonettini, S.; Prato, M.; Rebegoldi, S.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1335146
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