IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v124y2005i1d10.1007_s10957-004-6473-x.html
   My bibliography  Save this article

A Continuous Method for Convex Programming Problems

Author

Listed:
  • L. Z. Liao

    (Hong Kong Baptist University)

Abstract

In this paper, we present a continuous method for convex programming (CP) problems. Our approach converts first the convex problem into a monotone variational inequality (VI) problem. Then, a continuous method, which includes both a merit function and an ordinary differential equation (ODE), is introduced for the resulting variational inequality problem. The convergence of the ODE solution is proved for any starting point. There is no Lipschitz condition required in our proof. We show also that this limit point is an optimal solution for the original convex problem. Promising numerical results are presented.

Suggested Citation

  • L. Z. Liao, 2005. "A Continuous Method for Convex Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 124(1), pages 207-226, January.
    • Handle: RePEc:spr:joptap:v:124:y:2005:i:1:d:10.1007_s10957-004-6473-x
    DOI: 10.1007/s10957-004-6473-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-004-6473-x
    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/s10957-004-6473-x?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. B. S. He & L. Z. Liao, 2002. "Improvements of Some Projection Methods for Monotone Nonlinear Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 111-128, January.
    Full references (including those not matched with items on IDEAS)

    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. M.A. Noor, 2002. "Proximal Methods for Mixed Quasivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 115(2), pages 453-459, November.
    2. Bingsheng He & Li-Zhi Liao & Xiang Wang, 2012. "Proximal-like contraction methods for monotone variational inequalities in a unified framework I: Effective quadruplet and primary methods," Computational Optimization and Applications, Springer, vol. 51(2), pages 649-679, March.
    3. Bingsheng He & Li-Zhi Liao & Xiang Wang, 2012. "Proximal-like contraction methods for monotone variational inequalities in a unified framework II: general methods and numerical experiments," Computational Optimization and Applications, Springer, vol. 51(2), pages 681-708, March.
    4. Xingju Cai & Guoyong Gu & Bingsheng He, 2014. "On the O(1/t) convergence rate of the projection and contraction methods for variational inequalities with Lipschitz continuous monotone operators," Computational Optimization and Applications, Springer, vol. 57(2), pages 339-363, March.
    5. He, Bingsheng & He, Xiao-Zheng & Liu, Henry X. & Wu, Ting, 2009. "Self-adaptive projection method for co-coercive variational inequalities," European Journal of Operational Research, Elsevier, vol. 196(1), pages 43-48, July.
    6. M.A. Noor, 2002. "Proximal Methods for Mixed Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 115(2), pages 447-452, November.
    7. Hu Shao & William Lam & Mei Tam, 2006. "A Reliability-Based Stochastic Traffic Assignment Model for Network with Multiple User Classes under Uncertainty in Demand," Networks and Spatial Economics, Springer, vol. 6(3), pages 173-204, September.
    8. Min Tao & Xiaoming Yuan, 2012. "An inexact parallel splitting augmented Lagrangian method for monotone variational inequalities with separable structures," Computational Optimization and Applications, Springer, vol. 52(2), pages 439-461, June.
    9. Bing-sheng He & Wei Xu & Hai Yang & Xiao-Ming Yuan, 2011. "Solving Over-production and Supply-guarantee Problems in Economic Equilibria," Networks and Spatial Economics, Springer, vol. 11(1), pages 127-138, March.
    10. M. Li & H. Shao & B. He, 2007. "An inexact logarithmic-quadratic proximal augmented Lagrangian method for a class of constrained variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(2), pages 183-201, October.
    11. M.A. Noor, 2003. "Extragradient Methods for Pseudomonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 117(3), pages 475-488, June.
    12. Zhong-bao Wang & Xue Chen & Jiang Yi & Zhang-you Chen, 2022. "Inertial projection and contraction algorithms with larger step sizes for solving quasimonotone variational inequalities," Journal of Global Optimization, Springer, vol. 82(3), pages 499-522, March.
    13. Min Zhang & Deren Han & Gang Qian & Xihong Yan, 2012. "A New Decomposition Method for Variational Inequalities with Linear Constraints," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 675-695, March.
    14. Zhengyong Zhou & Bo Yu, 2014. "A smoothing homotopy method for variational inequality problems on polyhedral convex sets," Journal of Global Optimization, Springer, vol. 58(1), pages 151-168, January.
    15. Deren Han & Wei Xu & Hai Yang, 2010. "Solving a class of variational inequalities with inexact oracle operators," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(3), pages 427-452, June.
    16. He, Bingsheng & He, Xiao-Zheng & Liu, Henry X., 2010. "Solving a class of constrained 'black-box' inverse variational inequalities," European Journal of Operational Research, Elsevier, vol. 204(3), pages 391-401, August.
    17. Li, Min & Yuan, Xiao-Ming, 2008. "An APPA-based descent method with optimal step-sizes for monotone variational inequalities," European Journal of Operational Research, Elsevier, vol. 186(2), pages 486-495, April.
    18. K. Wang & D. R. Han & L. L. Xu, 2013. "A Parallel Splitting Method for Separable Convex Programs," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 138-158, 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:124:y:2005:i:1:d:10.1007_s10957-004-6473-x. 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.