Linear Convergence of Prox-SVRG Method for Separable Non-smooth Convex Optimization Problems under Bounded Metric Subregularity

Zhang, Jin1; Zhu, Xide2

2022

10.1007/s10957-021-01978-w

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS   影响因子和分区

0022-3239

1573-2878

With the help of bounded metric subregularity which is weaker than strong convexity, we show the linear convergence of proximal stochastic variance-reduced gradient (Prox-SVRG) method for solving a class of separable non-smooth convex optimization problems where the smooth item is a composite of strongly convex function and linear function. We introduce an equivalent characterization for the bounded metric subregularity by taking into account the calmness condition of a perturbed linear system. This equivalent characterization allows us to provide a verifiable sufficient condition to ensure linear convergence of Prox-SVRG and randomized block-coordinate proximal gradient methods. Furthermore, we verify that these sufficient conditions hold automatically when the non-smooth item is the generalized sparse group Lasso regularizer.

Linear convergence Bounded metric subregularity Calmness Proximal stochastic variance-reduced gradient Randomized block-coordinate proximal gradient

SCI

英语

第一

National Natural Science Foundation of China[11901380,11971220] ; Shenzhen Science and Technology Program[RCYX20200714114700072] ; Stable Support Plan Program of Shenzhen Natural Science Fund[20200925152128002] ; Guangdong Basic and Applied Basic Research Foundation[2019A1515011152] ; Shanghai Pujiang Program[2020PJC058]

Operations Research & Management Science ; Mathematics

Operations Research & Management Science ; Mathematics, Applied

WOS:000739271000003

SPRINGER/PLENUM PUBLISHERS

ENGINEERING

Web of Science

1.Southern Univ Sci & Technol, Natl Ctr Appl Math Shenzhen, Dept Math, Shenzhen, Peoples R China
2.Shanghai Univ, Sch Management, Shanghai, Peoples R China

Zhang, Jin,Zhu, Xide. Linear Convergence of Prox-SVRG Method for Separable Non-smooth Convex Optimization Problems under Bounded Metric Subregularity[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS,2022.

Zhang, Jin,&Zhu, Xide.(2022).Linear Convergence of Prox-SVRG Method for Separable Non-smooth Convex Optimization Problems under Bounded Metric Subregularity.JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS.

Zhang, Jin,et al."Linear Convergence of Prox-SVRG Method for Separable Non-smooth Convex Optimization Problems under Bounded Metric Subregularity".JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS (2022).