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

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  • 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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    1. Lukas Meier & Sara Van De Geer & Peter Bühlmann, 2008. "The group lasso for logistic regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 53-71, February.
    2. Jean-Pierre Aubin, 1984. "Lipschitz Behavior of Solutions to Convex Minimization Problems," Mathematics of Operations Research, INFORMS, vol. 9(1), pages 87-111, February.
    3. J. J. Ye & X. Y. Ye, 1997. "Necessary Optimality Conditions for Optimization Problems with Variational Inequality Constraints," Mathematics of Operations Research, INFORMS, vol. 22(4), pages 977-997, November.
    4. NESTEROV, Yurii, 2012. "Efficiency of coordinate descent methods on huge-scale optimization problems," LIDAM Reprints CORE 2511, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Stephen M. Robinson, 1980. "Strongly Regular Generalized Equations," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 43-62, February.
    6. P. Tseng & S. Yun, 2009. "Block-Coordinate Gradient Descent Method for Linearly Constrained Nonsmooth Separable Optimization," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 513-535, March.
    7. Ion Necoara & Yurii Nesterov & François Glineur, 2017. "Random Block Coordinate Descent Methods for Linearly Constrained Optimization over Networks," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 227-254, April.
    8. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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    Cited by:

    1. Cheik Traoré & Vassilis Apidopoulos & Saverio Salzo & Silvia Villa, 2024. "Variance Reduction Techniques for Stochastic Proximal Point Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1910-1939, November.

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