IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v95y1997i1d10.1023_a1022627226891.html
   My bibliography  Save this article

Smooth Transformation of the Generalized Minimax Problem

Author

Listed:
  • G. Di Pillo

    (Università di Roma “La Sapienza,”)

  • L. Grippo

    (Università di Roma “La Sapienza,”)

  • S. Lucidi

    (Università di Roma “La Sapienza,”)

Abstract

We consider the generalized minimax problem, that is, the problem of minimizing a function φ(x)=F(g 1(x),...,g m(x)), where F is a smooth function and each g i is the maximum of a finite number of smooth functions. We prove that, under suitable assumptions, it is possible to construct a continuously differentiable exact barrier function, whose minimizers yield the minimizers of the function φ. In this way, the nonsmooth original problem can be solved by usual minimization techniques for unconstrained differentiable functions.

Suggested Citation

  • G. Di Pillo & L. Grippo & S. Lucidi, 1997. "Smooth Transformation of the Generalized Minimax Problem," Journal of Optimization Theory and Applications, Springer, vol. 95(1), pages 1-24, October.
    • Handle: RePEc:spr:joptap:v:95:y:1997:i:1:d:10.1023_a:1022627226891
    DOI: 10.1023/A:1022627226891
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1022627226891
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1022627226891?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. Robert Mifflin, 1977. "An Algorithm for Constrained Optimization with Semismooth Functions," Mathematics of Operations Research, INFORMS, vol. 2(2), pages 191-207, May.
    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. Adam B. Levy, 2005. "Convergence of Successive Approximation Methods with Parameter Target Sets," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 765-784, August.
    2. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2022. "Essentials of numerical nonsmooth optimization," Annals of Operations Research, Springer, vol. 314(1), pages 213-253, July.
    3. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2006. "An Incremental Method for Solving Convex Finite Min-Max Problems," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 173-187, February.
    4. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2020. "Essentials of numerical nonsmooth optimization," 4OR, Springer, vol. 18(1), pages 1-47, March.

    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. Smail Addoune & Karima Boufi & Ahmed Roubi, 2018. "Proximal Bundle Algorithms for Nonlinearly Constrained Convex Minimax Fractional Programs," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 212-239, October.
    2. Churlzu Lim & Hanif Sherali, 2006. "A Trust Region Target Value Method for Optimizing Nondifferentiable Lagrangian Duals of Linear Programs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(1), pages 33-53, August.
    3. H. Boualam & A. Roubi, 2019. "Proximal bundle methods based on approximate subgradients for solving Lagrangian duals of minimax fractional programs," Journal of Global Optimization, Springer, vol. 74(2), pages 255-284, June.
    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. K. Kiwiel, 1994. "A Bundle of Method for Minimizing a Sum of Convex Functions with Smooth Weights," Working Papers wp94013, International Institute for Applied Systems Analysis.
    6. Hanif D. Sherali & Churlzu Lim, 2007. "Enhancing Lagrangian Dual Optimization for Linear Programs by Obviating Nondifferentiability," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 3-13, February.
    7. 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.
    8. Nezam Mahdavi-Amiri & Rohollah Yousefpour, 2012. "An Effective Nonsmooth Optimization Algorithm for Locally Lipschitz Functions," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 180-195, October.

    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:joptap:v:95:y:1997:i:1:d:10.1023_a:1022627226891. 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.