A new proximal heavy ball inexact line-search algorithm

S. Bonettini (), M. Prato and S. Rebegoldi
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S. Bonettini: Università degli Studi di Modena e Reggio Emilia
M. Prato: Università degli Studi di Modena e Reggio Emilia
S. Rebegoldi: Università degli Studi di Modena e Reggio Emilia

Computational Optimization and Applications, 2024, vol. 88, issue 2, No 5, 525-565

Abstract: Abstract We study a novel inertial proximal-gradient method for composite optimization. The proposed method alternates between a variable metric proximal-gradient iteration with 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.

Keywords: Forward-backward methods; Inertial methods; Line-search; Nonconvex optimization (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10589-024-00565-9

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