Convergence rate of a relaxed inertial proximal algorithm for convex minimization

Hedy Attouch () and Alexandre Cabot ()
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Hedy Attouch: IMAG - Institut Montpelliérain Alexander Grothendieck - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique
Alexandre Cabot: IMB - Institut de Mathématiques de Bourgogne [Dijon] - UB - Université de Bourgogne - CNRS - Centre National de la Recherche Scientifique

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Abstract: In a Hilbert space setting, the authors recently introduced a general class of relaxed inertial proximal algorithms that aim to solve monotone inclusions. In this paper, we specialize this study in the case of non-smooth convex minimization problems. We obtain convergence rates for values which have similarities with the results based on the Nesterov accelerated gradient method. The joint adjustment of inertia, relaxation and proximal terms plays a central role. In doing so, we highlight inertial proximal algorithms that converge for general monotone inclusions, and which, in the case of convex minimization, give fast convergence rates of values in the worst case.

Keywords: Inertial proximal method; Lyapunov analysis; maximally monotone operators; nonsmooth convex minimization; relaxation; maximal monotone-operators; weak-convergence; point algorithm; dynamics (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

Published in Optimization, 2020, 69 (6), pp.1281-1312. ⟨10.1080/02331934.2019.1696337⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02415789

DOI: 10.1080/02331934.2019.1696337

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