IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v78y2021i1d10.1007_s10589-020-00237-4.html
   My bibliography  Save this article

An efficient algorithm for nonconvex-linear minimax optimization problem and its application in solving weighted maximin dispersion problem

Author

Listed:
  • Weiwei Pan

    (Shanghai University)

  • Jingjing Shen

    (Shanghai University)

  • Zi Xu

    (Shanghai University)

Abstract

In this paper, we study the minimax optimization problem that is nonconvex in one variable and linear in the other variable, which is a special case of nonconvex-concave minimax problem, which has attracted significant attention lately due to their applications in modern machine learning tasks, signal processing and many other fields. We propose a new alternating gradient projection algorithm and prove that it can find an $$\varepsilon$$ ε -first-order stationary solution within $${\mathcal {O}}\left( \varepsilon ^{-3}\right)$$ O ε - 3 projected gradient step evaluations. Moreover, we apply it to solve the weighted maximin dispersion problem and the numerical results show that the proposed algorithm outperforms the state-of-the-art algorithms.

Suggested Citation

  • Weiwei Pan & Jingjing Shen & Zi Xu, 2021. "An efficient algorithm for nonconvex-linear minimax optimization problem and its application in solving weighted maximin dispersion problem," Computational Optimization and Applications, Springer, vol. 78(1), pages 287-306, January.
    • Handle: RePEc:spr:coopap:v:78:y:2021:i:1:d:10.1007_s10589-020-00237-4
    DOI: 10.1007/s10589-020-00237-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-020-00237-4
    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/s10589-020-00237-4?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.

    Citations

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


    Cited by:

    1. Lingzi Jin & Xiao Wang, 2022. "A stochastic primal-dual method for a class of nonconvex constrained optimization," Computational Optimization and Applications, Springer, vol. 83(1), pages 143-180, September.
    2. Siwen Wang & Zi Xu, 2021. "New Approximation Algorithms for Weighted Maximin Dispersion Problem with Box or Ball Constraints," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 524-539, August.
    3. Jiefei He & Huiling Zhang & Zi Xu, 2024. "An approximation proximal gradient algorithm for nonconvex-linear minimax problems with nonconvex nonsmooth terms," Journal of Global Optimization, Springer, vol. 90(1), pages 73-92, September.

    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:78:y:2021:i:1:d:10.1007_s10589-020-00237-4. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.