IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v66y2016i3d10.1007_s10898-016-0437-1.html
   My bibliography  Save this article

A primal–dual prediction–correction algorithm for saddle point optimization

Author

Listed:
  • Hongjin He

    (Hangzhou Dianzi University)

  • Jitamitra Desai

    (Nanyang Technological University)

  • Kai Wang

    (Nanyang Technological University)

Abstract

In this paper, we introduce a new primal–dual prediction–correction algorithm for solving a saddle point optimization problem, which serves as a bridge between the algorithms proposed in Cai et al. (J Glob Optim 57:1419–1428, 2013) and He and Yuan (SIAM J Imaging Sci 5:119–149, 2012). An interesting byproduct of the proposed method is that we obtain an easily implementable projection-based primal–dual algorithm, when the primal and dual variables belong to simple convex sets. Moreover, we establish the worst-case $${\mathcal {O}}(1/t)$$ O ( 1 / t ) convergence rate result in an ergodic sense, where t represents the number of iterations.

Suggested Citation

  • Hongjin He & Jitamitra Desai & Kai Wang, 2016. "A primal–dual prediction–correction algorithm for saddle point optimization," Journal of Global Optimization, Springer, vol. 66(3), pages 573-583, November.
    • Handle: RePEc:spr:jglopt:v:66:y:2016:i:3:d:10.1007_s10898-016-0437-1
    DOI: 10.1007/s10898-016-0437-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-016-0437-1
    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/s10898-016-0437-1?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. Guoyong Gu & Bingsheng He & Xiaoming Yuan, 2014. "Customized proximal point algorithms for linearly constrained convex minimization and saddle-point problems: a unified approach," Computational Optimization and Applications, Springer, vol. 59(1), pages 135-161, October.
    2. Xingju Cai & Deren Han & Lingling Xu, 2013. "An improved first-order primal-dual algorithm with a new correction step," Journal of Global Optimization, Springer, vol. 57(4), pages 1419-1428, December.
    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. Fan Jiang & Zhiyuan Zhang & Hongjin He, 2023. "Solving saddle point problems: a landscape of primal-dual algorithm with larger stepsizes," Journal of Global Optimization, Springer, vol. 85(4), pages 821-846, April.
    2. Yu, Yongchao & Peng, Jigen, 2018. "A modified primal-dual method with applications to some sparse recovery problems," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 76-94.

    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. Ying Gao & Wenxing Zhang, 2023. "An alternative extrapolation scheme of PDHGM for saddle point problem with nonlinear function," Computational Optimization and Applications, Springer, vol. 85(1), pages 263-291, May.
    2. Feng Ma, 2019. "On relaxation of some customized proximal point algorithms for convex minimization: from variational inequality perspective," Computational Optimization and Applications, Springer, vol. 73(3), pages 871-901, July.
    3. Yanqin Bai & Xiao Han & Tong Chen & Hua Yu, 2015. "Quadratic kernel-free least squares support vector machine for target diseases classification," Journal of Combinatorial Optimization, Springer, vol. 30(4), pages 850-870, November.
    4. Liusheng Hou & Hongjin He & Junfeng Yang, 2016. "A partially parallel splitting method for multiple-block separable convex programming with applications to robust PCA," Computational Optimization and Applications, Springer, vol. 63(1), pages 273-303, January.
    5. Eike Börgens & Christian Kanzow, 2019. "Regularized Jacobi-type ADMM-methods for a class of separable convex optimization problems in Hilbert spaces," Computational Optimization and Applications, Springer, vol. 73(3), pages 755-790, July.
    6. Fan Jiang & Zhiyuan Zhang & Hongjin He, 2023. "Solving saddle point problems: a landscape of primal-dual algorithm with larger stepsizes," Journal of Global Optimization, Springer, vol. 85(4), pages 821-846, April.
    7. Yu, Yongchao & Peng, Jigen, 2018. "A modified primal-dual method with applications to some sparse recovery problems," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 76-94.

    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:jglopt:v:66:y:2016:i:3:d:10.1007_s10898-016-0437-1. 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.