Proximal Gradient Algorithms Under Local Lipschitz Gradient Continuity

Alberto De Marchi () and Andreas Themelis ()
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Alberto De Marchi: Universität der Bundeswehr München
Andreas Themelis: Kyushu University

Journal of Optimization Theory and Applications, 2022, vol. 194, issue 3, No 2, 794 pages

Abstract: Abstract Composite optimization offers a powerful modeling tool for a variety of applications and is often numerically solved by means of proximal gradient methods. In this paper, we consider fully nonconvex composite problems under only local Lipschitz gradient continuity for the smooth part of the objective function. We investigate an adaptive scheme for PANOC-type methods (Stella et al. in Proceedings of the IEEE 56th CDC, 2017), namely accelerated linesearch algorithms requiring only the simple oracle of proximal gradient. While including the classical proximal gradient method, our theoretical results cover a broader class of algorithms and provide convergence guarantees for accelerated methods with possibly inexact computation of the proximal mapping. These findings have also significant practical impact, as they widen scope and performance of existing, and possibly future, general purpose optimization software that invoke PANOC as inner solver.

Keywords: Nonsmooth nonconvex optimization; Locally Lipschitz gradient; Forward–backward splitting; Linesearch methods; 49J52; 65K05; 90C30 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-022-02048-5

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