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

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-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.

This paper is in company with our recent work on Forward--Backward-type splitting methods http://arxiv.org/abs/1503.03703

References in corpus (1)

• Activity Identification and Local Linear Convergence of Forward--Backward-type methods

Cited by in corpus (3)

• ${\ell }_0$-Motivated Low-Rank Sparse Subspace Clustering
• Best Pair Formulation & Accelerated Scheme for Non-convex Principal Component Pursuit
• Convergence Rates of Inertial Splitting Schemes for Nonconvex Composite Optimization