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Subgradient Method for Nonconvex Nonsmooth Optimization

Author

Listed:
  • A. M. Bagirov

    (University of Ballarat)

  • L. Jin

    (University of Ballarat)

  • N. Karmitsa

    (University of Turku)

  • A. Al Nuaimat

    (University of Ballarat)

  • N. Sultanova

    (University of Ballarat)

Abstract

In this paper, we introduce a new method for solving nonconvex nonsmooth optimization problems. It uses quasisecants, which are subgradients computed in some neighborhood of a point. The proposed method contains simple procedures for finding descent directions and for solving line search subproblems. The convergence of the method is studied and preliminary results of numerical experiments are presented. The comparison of the proposed method with the subgradient and the proximal bundle methods is demonstrated using results of numerical experiments.

Suggested Citation

  • A. M. Bagirov & L. Jin & N. Karmitsa & A. Al Nuaimat & N. Sultanova, 2013. "Subgradient Method for Nonconvex Nonsmooth Optimization," Journal of Optimization Theory and Applications, Springer, vol. 157(2), pages 416-435, May.
    • Handle: RePEc:spr:joptap:v:157:y:2013:i:2:d:10.1007_s10957-012-0167-6
    DOI: 10.1007/s10957-012-0167-6
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    References listed on IDEAS

    as
    1. C. Beltran & F. J. Heredia, 2005. "An Effective Line Search for the Subgradient Method," Journal of Optimization Theory and Applications, Springer, vol. 125(1), pages 1-18, April.
    2. ANSTREICHER, Kurt M. & WOLSEY, Laurence A., 2009. "Two "well known" properties of subgradient optimization," LIDAM Reprints CORE 2102, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. A. M. Bagirov & B. Karasözen & M. Sezer, 2008. "Discrete Gradient Method: Derivative-Free Method for Nonsmooth Optimization," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 317-334, May.
    4. Adil Bagirov & Asef Ganjehlou, 2008. "An approximate subgradient algorithm for unconstrained nonsmooth, nonconvex optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(2), pages 187-206, April.
    5. A. Nedić & A. Ozdaglar, 2009. "Subgradient Methods for Saddle-Point Problems," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 205-228, July.
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    Cited by:

    1. Najmeh Hoseini Monjezi & S. Nobakhtian, 2021. "A filter proximal bundle method for nonsmooth nonconvex constrained optimization," Journal of Global Optimization, Springer, vol. 79(1), pages 1-37, January.
    2. Michael Herty & Sonja Steffensen & Anna Thunen, 2018. "Solving Quadratic Multi-Leader-Follower Games by Smoothing the Follower's Best Response," Papers 1808.07941, arXiv.org, revised Apr 2020.
    3. M. Alavi Hejazi & N. Movahedian & S. Nobakhtian, 2018. "On Constraint Qualifications and Sensitivity Analysis for General Optimization Problems via Pseudo-Jacobians," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 778-799, December.
    4. Maleknia, Morteza & Soleimani-damaneh, Majid, 2024. "An effective subgradient algorithm via Mifflin’s line search for nonsmooth nonconvex multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 319(2), pages 505-516.

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