1,489 research outputs found
A Multi-step Inertial Forward--Backward Splitting Method for Non-convex 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-{\L}ojasiewicz 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.Comment: This paper is in company with our recent work on
Forward--Backward-type splitting methods http://arxiv.org/abs/1503.0370
A Multi-step Inertial Forward-Backward Splitting Method for Non-convex Optimization
Abstract 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 algorithm 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 several problems arising from statistics and machine learning
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