IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v62y2015i1p183-203.html
   My bibliography  Save this article

D-gap functions and descent techniques for solving equilibrium problems

Author

Listed:
  • Giancarlo Bigi
  • Mauro Passacantando

Abstract

A new algorithm for solving equilibrium problems with differentiable bifunctions is provided. The algorithm is based on descent directions of a suitable family of D-gap functions. Its convergence is proved under assumptions which do not guarantee the equivalence between the stationary points of the D-gap functions and the solutions of the equilibrium problem. Moreover, the algorithm does not require to set parameters according to thresholds which depend on regularity properties of the equilibrium bifunction. The results of preliminary numerical tests on Nash equilibrium problems with quadratic payoffs are reported. Finally, some numerical comparisons with other D-gap algorithms are drawn relying on some further tests on linear equilibrium problems. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Giancarlo Bigi & Mauro Passacantando, 2015. "D-gap functions and descent techniques for solving equilibrium problems," Journal of Global Optimization, Springer, vol. 62(1), pages 183-203, May.
    • Handle: RePEc:spr:jglopt:v:62:y:2015:i:1:p:183-203
    DOI: 10.1007/s10898-014-0223-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-014-0223-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-014-0223-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. N. Yamashita & K. Taji & M. Fukushima, 1997. "Unconstrained Optimization Reformulations of Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 439-456, March.
    2. Bigi, Giancarlo & Castellani, Marco & Pappalardo, Massimo & Passacantando, Mauro, 2013. "Existence and solution methods for equilibria," European Journal of Operational Research, Elsevier, vol. 227(1), pages 1-11.
    3. Giancarlo Bigi & Mauro Passacantando, 2012. "Gap functions and penalization for solving equilibrium problems with nonlinear constraints," Computational Optimization and Applications, Springer, vol. 53(2), pages 323-346, October.
    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. Massimo Pappalardo & Giandomenico Mastroeni & Mauro Passacantando, 2016. "Merit functions: a bridge between optimization and equilibria," Annals of Operations Research, Springer, vol. 240(1), pages 271-299, 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. Massimo Pappalardo & Giandomenico Mastroeni & Mauro Passacantando, 2016. "Merit functions: a bridge between optimization and equilibria," Annals of Operations Research, Springer, vol. 240(1), pages 271-299, May.
    2. Giancarlo Bigi & Massimo Pappalardo & Mauro Passacantando, 2016. "Optimization Tools for Solving Equilibrium Problems with Nonsmooth Data," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 887-905, December.
    3. Toyasaki, Fuminori & Daniele, Patrizia & Wakolbinger, Tina, 2014. "A variational inequality formulation of equilibrium models for end-of-life products with nonlinear constraints," European Journal of Operational Research, Elsevier, vol. 236(1), pages 340-350.
    4. Giancarlo Bigi & Mauro Passacantando, 2015. "Descent and Penalization Techniques for Equilibrium Problems with Nonlinear Constraints," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 804-818, March.
    5. Giancarlo Bigi & Mauro Passacantando, 2016. "Gap functions for quasi-equilibria," Journal of Global Optimization, Springer, vol. 66(4), pages 791-810, December.
    6. Gábor Kassay & Mihaela Miholca, 2015. "Existence results for vector equilibrium problems given by a sum of two functions," Journal of Global Optimization, Springer, vol. 63(1), pages 195-211, September.
    7. L.R. Huang & K. F. Ng, 2005. "Equivalent Optimization Formulations and Error Bounds for Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 125(2), pages 299-314, May.
    8. M. Bianchi & G. Kassay & R. Pini, 2022. "Brezis pseudomonotone bifunctions and quasi equilibrium problems via penalization," Journal of Global Optimization, Springer, vol. 82(3), pages 483-498, March.
    9. Marco Castellani & Massimiliano Giuli & Massimo Pappalardo, 2018. "A Ky Fan Minimax Inequality for Quasiequilibria on Finite-Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 53-64, October.
    10. Riccardi, R. & Bonenti, F. & Allevi, E. & Avanzi, C. & Gnudi, A., 2015. "The steel industry: A mathematical model under environmental regulations," European Journal of Operational Research, Elsevier, vol. 242(3), pages 1017-1027.
    11. Thi Thu Van Nguyen & Jean Jacques Strodiot & Van Hien Nguyen, 2014. "Hybrid Methods for Solving Simultaneously an Equilibrium Problem and Countably Many Fixed Point Problems in a Hilbert Space," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 809-831, March.
    12. Somaye Jafari & Ali Farajzadeh & Sirous Moradi, 2016. "Locally Densely Defined Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 804-817, September.
    13. B. Qu & C. Y. Wang & J. Z. Zhang, 2003. "Convergence and Error Bound of a Method for Solving Variational Inequality Problems via the Generalized D-Gap Function," Journal of Optimization Theory and Applications, Springer, vol. 119(3), pages 535-552, December.
    14. Mircea Balaj & Dan Florin Serac, 2023. "Generalized Equilibrium Problems," Mathematics, MDPI, vol. 11(9), pages 1-11, May.
    15. Lorenzo Stella & Andreas Themelis & Panagiotis Patrinos, 2017. "Forward–backward quasi-Newton methods for nonsmooth optimization problems," Computational Optimization and Applications, Springer, vol. 67(3), pages 443-487, July.
    16. Jean Strodiot & Phan Vuong & Thi Nguyen, 2016. "A class of shrinking projection extragradient methods for solving non-monotone equilibrium problems in Hilbert spaces," Journal of Global Optimization, Springer, vol. 64(1), pages 159-178, January.
    17. Bijaya Kumar Sahu & Ouayl Chadli & Ram N. Mohapatra & Sabyasachi Pani, 2020. "Existence Results for Mixed Equilibrium Problems Involving Set-Valued Operators with Applications to Quasi-Hemivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 810-823, March.
    18. Chen, Li-Ming & Chang, Wei-Lun, 2020. "Under what conditions can an application service firm with in-house computing benefit from cloudbursting?," European Journal of Operational Research, Elsevier, vol. 282(1), pages 71-80.
    19. Yekini Shehu & Qiao-Li Dong & Lulu Liu & Jen-Chih Yao, 2023. "Alternated inertial subgradient extragradient method for equilibrium problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 1-30, April.
    20. K. F. Ng & L. L. Tan, 2007. "D-Gap Functions for Nonsmooth Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 133(1), pages 77-97, April.

    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:62:y:2015:i:1:p:183-203. 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.