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A Multi-step Inertial Forward--Backward Splitting Method for Non-convex Optimization

Jingwei Liang(jingwei.liang***at***ensicaen.fr)
Jalal Fadili(Jalal.Fadili***at***ensicaen.fr)
Gabriel Peyre(Gabriel.Peyre***at***ceremade.dauphine.fr)

Abstract: In this paper, we propose a multi-step inertial Forward--Backward splitting algorithm for minimizing the sum of two non-necessarily convex functions, one of which is proper lower semi-continuous while the other is differentiable with a Lipschitz continuous gradient. We first prove global convergence of the scheme with the help of the Kurdyka-Lojasiewicz property. Then, when the non-smooth part is also partly smooth relative to a smooth submanifold, we establish finite identification of the latter and provide sharp local linear convergence analysis. The proposed method is illustrated on a few problems arising from statistics and machine learning.

Keywords: Non-convex optimization, inertial Forward--Backward, Kurdyka-Lojasiewicz, Partial smoothness, Local linear convergence

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation:

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Entry Submitted: 06/06/2016
Entry Accepted: 06/06/2016
Entry Last Modified: 06/06/2016

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