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Modified Accelerated Bundle-Level Methods and Their Application in Two-Stage Stochastic Programming

Author

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  • Chunming Tang

    (College of Mathematics and Information Science, Guangxi University, Nanning 540004, China)

  • Bo He

    (College of Mathematics and Information Science, Guangxi University, Nanning 540004, China)

  • Zhenzhen Wang

    (College of Mathematics and Information Science, Guangxi University, Nanning 540004, China)

Abstract

The accelerated prox-level (APL) and uniform smoothing level (USL) methods recently proposed by Lan (Math Program, 149: 1–45, 2015) can achieve uniformly optimal complexity when solving black-box convex programming (CP) and structure non-smooth CP problems. In this paper, we propose two modified accelerated bundle-level type methods, namely, the modified APL (MAPL) and modified USL (MUSL) methods. Compared with the original APL and USL methods, the MAPL and MUSL methods reduce the number of subproblems by one in each iteration, thereby improving the efficiency of the algorithms. Conclusions of optimal iteration complexity of the proposed algorithms are established. Furthermore, the modified methods are applied to the two-stage stochastic programming, and numerical experiments are implemented to illustrate the advantages of our methods in terms of efficiency and accuracy.

Suggested Citation

  • Chunming Tang & Bo He & Zhenzhen Wang, 2020. "Modified Accelerated Bundle-Level Methods and Their Application in Two-Stage Stochastic Programming," Mathematics, MDPI, vol. 8(2), pages 1-26, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:265-:d:321548
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    References listed on IDEAS

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    1. Arthur F. Veinott, 1967. "The Supporting Hyperplane Method for Unimodal Programming," Operations Research, INFORMS, vol. 15(1), pages 147-152, February.
    2. 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.
    3. Jeff Linderoth & Alexander Shapiro & Stephen Wright, 2006. "The empirical behavior of sampling methods for stochastic programming," Annals of Operations Research, Springer, vol. 142(1), pages 215-241, February.
    4. 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).
    5. NESTEROV, Yu., 2005. "Smooth minimization of non-smooth functions," LIDAM Reprints CORE 1819, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Yang, Linfeng & Zhang, Chen & Jian, Jinbao & Meng, Ke & Xu, Yan & Dong, Zhaoyang, 2017. "A novel projected two-binary-variable formulation for unit commitment in power systems," Applied Energy, Elsevier, vol. 187(C), pages 732-745.
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