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A filter proximal bundle method for nonsmooth nonconvex constrained optimization

Author

Listed:
  • Najmeh Hoseini Monjezi

    (Faculty of Mathematics and Statistics, University of Isfahan)

  • S. Nobakhtian

    (Faculty of Mathematics and Statistics, University of Isfahan
    Institute for Research in Fundamental Sciences (IPM))

Abstract

A filter proximal bundle algorithm is presented for nonsmooth nonconvex constrained optimization problems. The new algorithm is based on the proximal bundle method and utilizes the improvement function to regularize the constraint. At every iteration by solving a convex piecewise-linear subproblem a trial point is obtained. The process of the filter technique is employed either to accept the trial point as a serious iterate or to reject it as a null iterate. Under some mild and standard assumptions and for every possible choice of a starting point, it is shown that every accumulation point of the sequence of serious iterates is feasible. In addition, there exists at least one accumulation point which is stationary for the improvement function. Finally, some encouraging numerical results show that the proposed algorithm is effective.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:79:y:2021:i:1:d:10.1007_s10898-020-00939-3
    DOI: 10.1007/s10898-020-00939-3
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    References listed on IDEAS

    as
    1. Yang Yang & Liping Pang & Xuefei Ma & Jie Shen, 2014. "Constrained Nonconvex Nonsmooth Optimization via Proximal Bundle Method," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 900-925, December.
    2. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico & Adil M. Bagirov, 2018. "Minimizing nonsmooth DC functions via successive DC piecewise-affine approximations," Journal of Global Optimization, Springer, vol. 71(1), pages 37-55, May.
    3. Kaisa Joki & Adil M. Bagirov & Napsu Karmitsa & Marko M. Mäkelä, 2017. "A proximal bundle method for nonsmooth DC optimization utilizing nonconvex cutting planes," Journal of Global Optimization, Springer, vol. 68(3), pages 501-535, July.
    4. 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.
    5. Najmeh Hoseini Monjezi & S. Nobakhtian, 2019. "A new infeasible proximal bundle algorithm for nonsmooth nonconvex constrained optimization," Computational Optimization and Applications, Springer, vol. 74(2), pages 443-480, November.
    6. 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.
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