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

Jin Zhang () and Xide Zhu ()
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Jin Zhang: Southern University of Science and Technology, National Center for Applied Mathematics Shenzhen
Xide Zhu: Shanghai University

Journal of Optimization Theory and Applications, 2022, vol. 192, issue 2, No 7, 564-597

Abstract: Abstract 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.

Keywords: Linear convergence; Bounded metric subregularity; Calmness; Proximal stochastic variance-reduced gradient; Randomized block-coordinate proximal gradient; 90C06; 90C25; 90C52 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-021-01978-w

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