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

Author

Listed:
  • Jin Zhang

    (Southern University of Science and Technology, National Center for Applied Mathematics Shenzhen)

  • Xide Zhu

    (Shanghai University)

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.

Suggested Citation

  • Jin Zhang & Xide Zhu, 2022. "Linear Convergence of Prox-SVRG Method for Separable Non-smooth Convex Optimization Problems under Bounded Metric Subregularity," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 564-597, February.
    • Handle: RePEc:spr:joptap:v:192:y:2022:i:2:d:10.1007_s10957-021-01978-w
    DOI: 10.1007/s10957-021-01978-w
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    References listed on IDEAS

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