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A dual-based stochastic inexact algorithm for a class of stochastic nonsmooth convex composite problems

Author

Listed:
  • Gui-Hua Lin

    (Shanghai University)

  • Zhen-Ping Yang

    (Jiaying University)

  • Hai-An Yin

    (Southern University of Science and Technology)

  • Jin Zhang

    (Peng Cheng Laboratory)

Abstract

In this paper, a dual-based stochastic inexact algorithm is developed to solve a class of stochastic nonsmooth convex problems with underlying structure. This algorithm can be regarded as an integration of a deterministic augmented Lagrangian method and some stochastic approximation techniques. By utilizing the sparsity of the second order information, each subproblem is efficiently solved by a superlinearly convergent semismooth Newton method. We derive some almost surely convergence properties and convergence rate of objective values. Furthermore, we present some results related to convergence rate of distance between iteration points and solution set under error bound conditions. Numerical results demonstrate favorable comparison of the proposed algorithm with some existing methods.

Suggested Citation

  • Gui-Hua Lin & Zhen-Ping Yang & Hai-An Yin & Jin Zhang, 2023. "A dual-based stochastic inexact algorithm for a class of stochastic nonsmooth convex composite problems," Computational Optimization and Applications, Springer, vol. 86(2), pages 669-710, November.
    • Handle: RePEc:spr:coopap:v:86:y:2023:i:2:d:10.1007_s10589-023-00504-0
    DOI: 10.1007/s10589-023-00504-0
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    References listed on IDEAS

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    3. Xiantao Xiao, 2021. "A Unified Convergence Analysis of Stochastic Bregman Proximal Gradient and Extragradient Methods," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 605-627, March.
    4. R. T. Rockafellar, 1976. "Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 97-116, May.
    5. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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