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

Jingwei Liang · Jalal Fadili · Gabriel Peyré

Area 5+6+7+8 #73

Keywords: [ Nonlinear Dimension Reduction and Manifold Learning ] [ Sparsity and Feature Selection ] [ (Other) Optimization ]


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–Łojasiewicz 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.

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