Proximal Gradient Algorithms Under Local Lipschitz Gradient Continuity A Convergence and Robustness Analysis of PANOC

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 objectiv...

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Veröffentlicht in:Journal of optimization theory and applications Jg. 194; H. 3; S. 771 - 794
Hauptverfasser: De Marchi, Alberto, Themelis, Andreas
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.09.2022
Schlagworte:
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Engineering
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Theory of Computation
65K05
90C30
49J52
Locally Lipschitz gradient
Nonsmooth nonconvex optimization
Forward–backward splitting
Linesearch methods
ISSN:0022-3239, 1573-2878
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Zusammenfassung: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.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-022-02048-5