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Journal Articles Mathematical Programming, Series A Year : 2018

Convergence rate of inertial Forward-Backward algorithm beyond Nesterov's rule

Abstract

In this paper we study the convergence of an Inertial Forward-Backward algorithm, with a particular choice of an over-relaxation term. In particular we show that for a sequence of overrrelaxation parameters, that do not satisfy Nesterov’s rule one can still expect some relatively fast convergence properties for the objective function. In addition we complement this work by studying the convergence of the algorithm in the case where the proximal operator is inexactly computed with the presence of some errors and we give sufficient conditions over these errors in order to obtain some convergence properties for the objective function .
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Dates and versions

hal-01551873 , version 1 (30-06-2017)

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Vassilis Apidopoulos, Jean-François Aujol, Charles H Dossal. Convergence rate of inertial Forward-Backward algorithm beyond Nesterov's rule. Mathematical Programming, Series A, 2018, pp.1-20. ⟨10.1007/s10107-018-1350-9⟩. ⟨hal-01551873⟩
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