IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v73y2019i4d10.1007_s10898-018-00735-0.html
   My bibliography  Save this article

A subgradient algorithm for a class of nonlinear split feasibility problems: application to jointly constrained Nash equilibrium models

Author

Listed:
  • Le Hai Yen

    (VAST)

  • Nguyen Thi Thanh Huyen

    (Thainguyen University of Sciences)

  • Le Dung Muu

    (VAST)

Abstract

In this paper we propose an algorithm for solving the split feasibility problem $$x\in C, Ax\in Q$$ x ∈ C , A x ∈ Q with C being the solution set of an equilibrium problem and A can be nonlinear. The proposed algorithm is a combination between the projection method for the equilibrium problem and the gradient method for the inclusion $$Ax\in Q$$ A x ∈ Q . The convergence of the algorithm is investigated. A numerical example for a jointly constrained Nash equilibrium model in electricity production market is provided to demonstrate the behavior of the algorithm.

Suggested Citation

  • Le Hai Yen & Nguyen Thi Thanh Huyen & Le Dung Muu, 2019. "A subgradient algorithm for a class of nonlinear split feasibility problems: application to jointly constrained Nash equilibrium models," Journal of Global Optimization, Springer, vol. 73(4), pages 849-868, April.
    • Handle: RePEc:spr:jglopt:v:73:y:2019:i:4:d:10.1007_s10898-018-00735-0
    DOI: 10.1007/s10898-018-00735-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-018-00735-0
    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/s10898-018-00735-0?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. Steffan Berridge & Jacek Krawczyk, "undated". "Relaxation Algorithms in Finding Nash Equilibrium," Computing in Economics and Finance 1997 159, Society for Computational Economics.
    2. WEI, Jing-Yuan & SMEERS, Yves, 1999. "Spatial oligopolistic electricity models with Cournot generators and regulated transmission prices," LIDAM Reprints CORE 1454, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. A. Moudafi, 2011. "Split Monotone Variational Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 275-283, August.
    4. 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.
    5. Abdellah Bnouhachem & Muhammad Noor & Mohamed Khalfaoui & Sheng Zhaohan, 2012. "On descent-projection method for solving the split feasibility problems," Journal of Global Optimization, Springer, vol. 54(3), pages 627-639, November.
    6. Wei Jing-Yuan & Yves Smeers, 1999. "Spatial Oligopolistic Electricity Models with Cournot Generators and Regulated Transmission Prices," Operations Research, INFORMS, vol. 47(1), pages 102-112, 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. Qiao-Li Dong & Songnian He & Michael Th. Rassias, 2021. "General splitting methods with linearization for the split feasibility problem," Journal of Global Optimization, Springer, vol. 79(4), pages 813-836, April.

    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. Benjamin F. Hobbs & J. S. Pang, 2007. "Nash-Cournot Equilibria in Electric Power Markets with Piecewise Linear Demand Functions and Joint Constraints," Operations Research, INFORMS, vol. 55(1), pages 113-127, February.
    2. Francisco Facchinei & Christian Kanzow, 2010. "Generalized Nash Equilibrium Problems," Annals of Operations Research, Springer, vol. 175(1), pages 177-211, March.
    3. Steven A. Gabriel & Supat Kiet & Jifang Zhuang, 2005. "A Mixed Complementarity-Based Equilibrium Model of Natural Gas Markets," Operations Research, INFORMS, vol. 53(5), pages 799-818, October.
    4. Andreas Ehrenmann & Karsten Neuhoff, 2009. "A Comparison of Electricity Market Designs in Networks," Operations Research, INFORMS, vol. 57(2), pages 274-286, April.
    5. Cristian Zambrano & Yris Olaya, 2017. "An agent-based simulation approach to congestion management for the Colombian electricity market," Annals of Operations Research, Springer, vol. 258(2), pages 217-236, November.
    6. Lise, Wietze & Linderhof, Vincent & Kuik, Onno & Kemfert, Claudia & Ostling, Robert & Heinzow, Thomas, 2006. "A game theoretic model of the Northwestern European electricity market--market power and the environment," Energy Policy, Elsevier, vol. 34(15), pages 2123-2136, October.
    7. Contreras, Javier & Krawczyk, Jacek & Zuccollo, James, 2008. "Can planners control competitive generators?," MPRA Paper 10395, University Library of Munich, Germany.
    8. Migot, Tangi & Cojocaru, Monica-G., 2020. "A parametrized variational inequality approach to track the solution set of a generalized nash equilibrium problem," European Journal of Operational Research, Elsevier, vol. 283(3), pages 1136-1147.
    9. Thidaporn Seangwattana & Somyot Plubtieng & Kanokwan Sitthithakerngkiet, 2021. "A new linesearch iterative scheme for finding a common solution of split equilibrium and fixed point problems," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(2), pages 614-628, June.
    10. Heikki Peura & Derek W. Bunn, 2015. "Dynamic Pricing of Peak Production," Operations Research, INFORMS, vol. 63(6), pages 1262-1279, December.
    11. Petropoulos, Georgios & Willems, Bert, 2020. "Long-term transmission rights and dynamic efficiency," Energy Economics, Elsevier, vol. 88(C).
    12. Rossana Riccardi & Giorgia Oggioni & Elisabetta Allevi & Abdel Lisser, 2023. "Complementarity formulation of games with random payoffs," Computational Management Science, Springer, vol. 20(1), pages 1-32, December.
    13. Elisabetta Allevi & Adriana Gnudi & Igor V. Konnov & Giorgia Oggioni, 2017. "Dynamic Spatial Auction Market Models with General Cost Mappings," Networks and Spatial Economics, Springer, vol. 17(2), pages 367-403, June.
    14. Han, Deren & Zhang, Hongchao & Qian, Gang & Xu, Lingling, 2012. "An improved two-step method for solving generalized Nash equilibrium problems," European Journal of Operational Research, Elsevier, vol. 216(3), pages 613-623.
    15. Yihsu Chen & Andrew L. Liu & Benjamin F. Hobbs, 2011. "Economic and Emissions Implications of Load-Based, Source-Based, and First-Seller Emissions Trading Programs Under California AB32," Operations Research, INFORMS, vol. 59(3), pages 696-712, June.
    16. Krebs, Vanessa & Schewe, Lars & Schmidt, Martin, 2018. "Uniqueness and multiplicity of market equilibria on DC power flow networks," European Journal of Operational Research, Elsevier, vol. 271(1), pages 165-178.
    17. M. Castellani & M. Giuli, 2019. "A coercivity condition for nonmonotone quasiequilibria on finite-dimensional spaces," Journal of Global Optimization, Springer, vol. 75(1), pages 163-176, September.
    18. E. J. Anderson & A. B. Philpott, 2002. "Using Supply Functions for Offering Generation into an Electricity Market," Operations Research, INFORMS, vol. 50(3), pages 477-489, June.
    19. Huang, Yongxi & Chen, Yihsu, 2014. "Analysis of an imperfectly competitive cellulosic biofuel supply chain," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 72(C), pages 1-14.
    20. Le Hai Yen & Le Dung Muu & Nguyen Thi Thanh Huyen, 2016. "An algorithm for a class of split feasibility problems: application to a model in electricity production," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(3), pages 549-565, December.

    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:73:y:2019:i:4:d:10.1007_s10898-018-00735-0. 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.