IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v101y1999i1d10.1023_a1021727228957.html
   My bibliography  Save this article

Combined Entropic Regularization and Path-Following Method for Solving Finite Convex Min-max Problems Subject to Infinitely Many Linear Constraints

Author

Listed:
  • R. L. Sheu

    (National Cheng-Kung University)

  • S. Y. Wu

    (National Cheng-Kung University)

Abstract

In this paper, we study the minimization of the max function of q smooth convex functions on a domain specified by infinitely many linear constraints. The difficulty of such problems arises from the kinks of the max function and it is often suggested that, by imposing certain regularization functions, nondifferentiability will be overcome. We find that the entropic regularization introduced by Li and Fang is closely related to recently developed path-following interior-point methods. Based on their results, we create an interior trajectory in the feasible domain and propose a path-following algorithm with a convergence proof. Our intention here is to show a nice combination of minmax problems, semi-infinite programming, and interior-point methods. Hopefully, this will lead to new applications.

Suggested Citation

  • R. L. Sheu & S. Y. Wu, 1999. "Combined Entropic Regularization and Path-Following Method for Solving Finite Convex Min-max Problems Subject to Infinitely Many Linear Constraints," Journal of Optimization Theory and Applications, Springer, vol. 101(1), pages 167-190, April.
    • Handle: RePEc:spr:joptap:v:101:y:1999:i:1:d:10.1023_a:1021727228957
    DOI: 10.1023/A:1021727228957
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1021727228957
    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:1021727228957?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. Xing-Si Li & Shu-Cherng Fang, 1997. "On the entropic regularization method for solving min-max problems with applications," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(1), pages 119-130, February.
    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. Alfred Auslender & Miguel A. Goberna & Marco A. López, 2009. "Penalty and Smoothing Methods for Convex Semi-Infinite Programming," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 303-319, May.

    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. Birbil, S.I. & Fang, S-C. & Han, J., 2002. "Entropic Regularization Approach for Mathematical Programs with Equilibrium Constraints," ERIM Report Series Research in Management ERS-2002-71-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    2. Alidaee, Bahram, 2014. "Zero duality gap in surrogate constraint optimization: A concise review of models," European Journal of Operational Research, Elsevier, vol. 232(2), pages 241-248.
    3. Birbil, S.I. & Fang, S-C. & Han, J., 2002. "Entropic regularization approach for mathematical programs with equilibrium constraints," Econometric Institute Research Papers EI 2002-52, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    4. Xide Zhu & Peijun Guo, 2017. "Approaches to four types of bilevel programming problems with nonconvex nonsmooth lower level programs and their applications to newsvendor problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(2), pages 255-275, October.
    5. Helene Krieg & Tobias Seidel & Jan Schwientek & Karl-Heinz Küfer, 2022. "Solving continuous set covering problems by means of semi-infinite optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(1), pages 39-82, August.
    6. Fusheng Wang & Kecun Zhang, 2008. "A hybrid algorithm for nonlinear minimax problems," Annals of Operations Research, Springer, vol. 164(1), pages 167-191, November.

    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:101:y:1999:i:1:d:10.1023_a:1021727228957. 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.