On the Proximal Gradient Algorithm with Alternated Inertia

Franck Iutzeler () and Jérôme Malick ()
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Franck Iutzeler: University of Grenoble Alpes
Jérôme Malick: CNRS, LJK

Journal of Optimization Theory and Applications, 2018, vol. 176, issue 3, No 9, 688-710

Abstract: Abstract 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.

Keywords: Proximal gradient algorithm; Accelerated methods; Kurdyka–Łojasiewicz inequality; 65K10; 90C30 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10957-018-1226-4

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