On the Proximal Gradient Algorithm with Alternated Inertia

In this paper, we investigate attractive properties of the proximal gradient algorithm with inertia. Notably, we show that using alternated inertia yields monotonically decreasing functional values, which contrasts with usual accelerated proximal gradient methods. We also provide convergence rates f...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 176; no. 3; pp. 688 - 710
Main Authors: Iutzeler, Franck, Malick, Jérôme
Format: Journal Article
Language:English
Published: New York Springer US 01.03.2018
Springer Nature B.V
Springer Verlag
Subjects:
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Economic models
Engineering
Inertia
Machine Learning
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Optimization and Control
Statistics
Theory of Computation
65K10
90C30
Proximal gradient algorithm
Accelerated methods
Kurdyka–Łojasiewicz inequality
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:In this paper, we investigate attractive properties of the proximal gradient algorithm with inertia. Notably, we show that using alternated inertia yields monotonically decreasing functional values, which contrasts with usual accelerated proximal gradient methods. We also provide convergence rates for the algorithm with alternated inertia, based on local geometric properties of the objective function. The results are put into perspective by discussions on several extensions (strongly convex case, non-convex case, and alternated extrapolation) and illustrations on common regularized optimization problems.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-018-1226-4