On Globally Q-Linear Convergence of a Splitting Method for Group Lasso

doi:https://doi.org/10.1007/s40305-017-0176-0

Journal of the Operations Research Society of China ›› 2018, Vol. 6 ›› Issue (3): 445-454.doi: https://doi.org/10.1007/s40305-017-0176-0

所属专题： Continuous Optimization

出版日期:2018-09-30 发布日期:2018-09-30

On Globally Q-Linear Convergence of a Splitting Method for Group Lasso

Yun-Da Dong¹，Hai-Bin Zhang²， Huan Gao^2,3

1 School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
2 College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
3 College of Mathematics and Computational Science, Hunan First Normal University,Changsha 410205, China

Online:2018-09-30 Published:2018-09-30
Supported by:
This research was supported by the National Natural Science Foundation of China (No. 61179033), and Collaborative Innovation Center on Beijing Society-Building and Social Governance.

摘要/Abstract

Abstract:

In this paper, we discuss a splitting method for group Lasso. By assuming that the sequence of the step lengths has positive lower bound and positive upper bound (unrelated to the given problem data), we prove its Q-linear rate of convergence of the distance sequence of the iterates to the solution set. Moreover, we make comparisons with convergence of the proximal gradient method analyzed very recently.

Key words: Group Lasso ·, Splitting method ·, Proximal gradient method ·, Q-linear rate of convergence

. [J]. Journal of the Operations Research Society of China, 2018, 6(3): 445-454.

Yun-Da Dong, Hai-Bin Zhang, Huan Gao. On Globally Q-Linear Convergence of a Splitting Method for Group Lasso[J]. Journal of the Operations Research Society of China, 2018, 6(3): 445-454.

On Globally Q-Linear Convergence of a Splitting Method for Group Lasso

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