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A multi-step doubly stabilized bundle method for nonsmooth convex optimization

Author

Listed:
  • Tang, Chunming
  • Liu, Shuai
  • Jian, Jinbao
  • Ou, Xiaomei

Abstract

In this paper, by incorporating a multi-step scheme into the doubly stabilized bundle method (DSBM) recently developed by Oliveira and Solodov (2016), we propose a multi-step doubly stabilized bundle method (MDSBM) for solving nonsmooth convex optimization problems. In contrast to a single sequence generated by DSBM, the MDSBM generates three related iteration sequences. One is used to build the cutting-planes model of the objective function, another is served as the stability centers, and the third is the sequence of solutions to our new doubly stabilized subproblems. In addition, we present a new descent test criterion, aiming to take advantage of the multi-step scheme. We establish global convergence of the proposed method, and finally present some promising numerical results.

Suggested Citation

  • Tang, Chunming & Liu, Shuai & Jian, Jinbao & Ou, Xiaomei, 2020. "A multi-step doubly stabilized bundle method for nonsmooth convex optimization," Applied Mathematics and Computation, Elsevier, vol. 376(C).
    • Handle: RePEc:eee:apmaco:v:376:y:2020:i:c:s0096300320301235
    DOI: 10.1016/j.amc.2020.125154
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    References listed on IDEAS

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    1. W. Hare & C. Sagastizábal & M. Solodov, 2016. "A proximal bundle method for nonsmooth nonconvex functions with inexact information," Computational Optimization and Applications, Springer, vol. 63(1), pages 1-28, January.
    2. Jian Lv & Li-Ping Pang & Fan-Yun Meng, 2018. "A proximal bundle method for constrained nonsmooth nonconvex optimization with inexact information," Journal of Global Optimization, Springer, vol. 70(3), pages 517-549, March.
    3. Li-Ping Pang & Jian Lv & Jin-He Wang, 2016. "Constrained incremental bundle method with partial inexact oracle for nonsmooth convex semi-infinite programming problems," Computational Optimization and Applications, Springer, vol. 64(2), pages 433-465, June.
    4. Yunmei Chen & Guanghui Lan & Yuyuan Ouyang & Wei Zhang, 2019. "Fast bundle-level methods for unconstrained and ball-constrained convex optimization," Computational Optimization and Applications, Springer, vol. 73(1), pages 159-199, May.
    5. K. C. Kiwiel, 2000. "Efficiency of Proximal Bundle Methods," Journal of Optimization Theory and Applications, Springer, vol. 104(3), pages 589-603, March.
    6. Shuai Liu, 2019. "A simple version of bundle method with linear programming," Computational Optimization and Applications, Springer, vol. 72(2), pages 391-412, March.
    7. Tang, Chun-ming & Jian, Jin-bao, 2012. "Strongly sub-feasible direction method for constrained optimization problems with nonsmooth objective functions," European Journal of Operational Research, Elsevier, vol. 218(1), pages 28-37.
    8. Wim Ackooij & Welington Oliveira, 2014. "Level bundle methods for constrained convex optimization with various oracles," Computational Optimization and Applications, Springer, vol. 57(3), pages 555-597, April.
    9. Lemaréchal, C. & Nemirovskii, A. & Nesterov, Y., 1995. "New variants of bundle methods," LIDAM Reprints CORE 1166, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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