IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v74y2019i2d10.1007_s10589-019-00115-8.html
   My bibliography  Save this article

A new infeasible proximal bundle algorithm for nonsmooth nonconvex constrained optimization

Author

Listed:
  • Najmeh Hoseini Monjezi

    (University of Isfahan)

  • S. Nobakhtian

    (University of Isfahan
    Institute for Research in Fundamental Sciences (IPM))

Abstract

Proximal bundle method has usually been presented for unconstrained convex optimization problems. In this paper, we develop an infeasible proximal bundle method for nonsmooth nonconvex constrained optimization problems. Using the improvement function we transform the problem into an unconstrained one and then we build a cutting plane model. The resulting algorithm allows effective control of the size of quadratic programming subproblems via the aggregation techniques. The novelty in our approach is that the objective and constraint functions can be any arbitrary (regular) locally Lipschitz functions. In addition the global convergence, starting from any point, is proved in the sense that every accumulation point of the iterative sequence is stationary for the improvement function. At the end, some encouraging numerical results with a MATLAB implementation are also reported.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:74:y:2019:i:2:d:10.1007_s10589-019-00115-8
    DOI: 10.1007/s10589-019-00115-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-019-00115-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10589-019-00115-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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. Krzysztof Czesław Kiwiel, 1985. "A Linearization Algorithm for Nonsmooth Minimization," Mathematics of Operations Research, INFORMS, vol. 10(2), pages 185-194, May.
    3. Minh N. Dao & Joachim Gwinner & Dominikus Noll & Nina Ovcharova, 2016. "Nonconvex bundle method with application to a delamination problem," Computational Optimization and Applications, Springer, vol. 65(1), pages 173-203, September.
    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. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. N. Hoseini Monjezi & S. Nobakhtian, 2022. "An inexact multiple proximal bundle algorithm for nonsmooth nonconvex multiobjective optimization problems," Annals of Operations Research, Springer, vol. 311(2), pages 1123-1154, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xiaoliang Wang & Liping Pang & Qi Wu & Mingkun Zhang, 2021. "An Adaptive Proximal Bundle Method with Inexact Oracles for a Class of Nonconvex and Nonsmooth Composite Optimization," Mathematics, MDPI, vol. 9(8), pages 1-27, April.
    2. Wim Ackooij & Welington Oliveira, 2019. "Nonsmooth and Nonconvex Optimization via Approximate Difference-of-Convex Decompositions," Journal of Optimization Theory and Applications, Springer, vol. 182(1), pages 49-80, July.
    3. 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.
    4. 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.
    5. Fan-Yun Meng & Li-Ping Pang & Jian Lv & Jin-He Wang, 2017. "An approximate bundle method for solving nonsmooth equilibrium problems," Journal of Global Optimization, Springer, vol. 68(3), pages 537-562, July.
    6. Welington Oliveira, 2019. "Proximal bundle methods for nonsmooth DC programming," Journal of Global Optimization, Springer, vol. 75(2), pages 523-563, October.
    7. Li-Ping Pang & Fan-Yun Meng & Jian-Song Yang, 2023. "A class of infeasible proximal bundle methods for nonsmooth nonconvex multi-objective optimization problems," Journal of Global Optimization, Springer, vol. 85(4), pages 891-915, April.
    8. Ouayl Chadli & Joachim Gwinner & M. Zuhair Nashed, 2022. "Noncoercive Variational–Hemivariational Inequalities: Existence, Approximation by Double Regularization, and Application to Nonmonotone Contact Problems," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 42-65, June.
    9. W. Ackooij & S. Demassey & P. Javal & H. Morais & W. Oliveira & B. Swaminathan, 2021. "A bundle method for nonsmooth DC programming with application to chance-constrained problems," Computational Optimization and Applications, Springer, vol. 78(2), pages 451-490, March.
    10. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2023. "Sparse optimization via vector k-norm and DC programming with an application to feature selection for support vector machines," Computational Optimization and Applications, Springer, vol. 86(2), pages 745-766, November.
    11. 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.
    12. M. V. Dolgopolik, 2020. "New global optimality conditions for nonsmooth DC optimization problems," Journal of Global Optimization, Springer, vol. 76(1), pages 25-55, January.
    13. Minh N. Dao & Joachim Gwinner & Dominikus Noll & Nina Ovcharova, 2016. "Nonconvex bundle method with application to a delamination problem," Computational Optimization and Applications, Springer, vol. 65(1), pages 173-203, September.
    14. Pang, Li-Ping & Chen, Shuang & Wang, Jin-He, 2015. "Risk management in portfolio applications of non-convex stochastic programming," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 565-575.
    15. 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.
    16. A. M. Bagirov & N. Hoseini Monjezi & S. Taheri, 2021. "An augmented subgradient method for minimizing nonsmooth DC functions," Computational Optimization and Applications, Springer, vol. 80(2), pages 411-438, November.
    17. Hoai An Le Thi & Vinh Thanh Ho & Tao Pham Dinh, 2019. "A unified DC programming framework and efficient DCA based approaches for large scale batch reinforcement learning," Journal of Global Optimization, Springer, vol. 73(2), pages 279-310, February.
    18. 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.
    19. Jie Shen & Ya-Li Gao & Fang-Fang Guo & Rui Zhao, 2018. "A Redistributed Bundle Algorithm for Generalized Variational Inequality Problems in Hilbert Spaces," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(04), pages 1-18, August.
    20. 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).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:coopap:v:74:y:2019:i:2:d:10.1007_s10589-019-00115-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.