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

Part of Advances in Neural Information Processing Systems 29 (NIPS 2016)

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Jingwei Liang, Jalal Fadili, Gabriel Peyré


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.