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Article Dans Une Revue Optimization Année : 2020

Convergence rate of a relaxed inertial proximal algorithm for convex minimization

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Résumé

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.

Dates et versions

hal-02415789 , version 1 (17-12-2019)

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Hedy Attouch, Alexandre Cabot. Convergence rate of a relaxed inertial proximal algorithm for convex minimization. Optimization, 2020, 69 (6), pp.1281-1312. ⟨10.1080/02331934.2019.1696337⟩. ⟨hal-02415789⟩
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