IDEAS home Printed from https://ideas.repec.org/a/spr/indpam/v50y2019i4d10.1007_s13226-019-0363-2.html
   My bibliography  Save this article

Viscosity extragradient method with Armijo linesearch rule for pseudomonotone equilibrium problem and fixed point problem in Hilbert spaces

Author

Listed:
  • Gaobo Li

    (Shan Dong Women’s University)

  • Yanxia Lu

    (North China Electric Power University)

  • Yeol Je Cho

    (Gyeongsang National University
    University of Electronic Science and Technology of China)

Abstract

In this paper, we introduce a viscosity extragradient method with Armijo linesearch rule to find a common element of solution set of a pseudomonotone equilibrium problem and fixed point set of a nonexpansive nonself-mapping in Hilbert space. The strong convergence of the algorithm is proved. As the application, a common fixed point theorem for two nonexpansive nonself-mappings is proved. Finally, some numerical examples are given to illustrate the effectiveness of the algorithm. Our result improves the ones of others in the literature.

Suggested Citation

  • Gaobo Li & Yanxia Lu & Yeol Je Cho, 2019. "Viscosity extragradient method with Armijo linesearch rule for pseudomonotone equilibrium problem and fixed point problem in Hilbert spaces," Indian Journal of Pure and Applied Mathematics, Springer, vol. 50(4), pages 903-921, December.
    • Handle: RePEc:spr:indpam:v:50:y:2019:i:4:d:10.1007_s13226-019-0363-2
    DOI: 10.1007/s13226-019-0363-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13226-019-0363-2
    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/s13226-019-0363-2?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. P. Anh & H. Le Thi, 2013. "An Armijo-type method for pseudomonotone equilibrium problems and its applications," Journal of Global Optimization, Springer, vol. 57(3), pages 803-820, November.
    2. Dong, June & Zhang, Ding & Nagurney, Anna, 2004. "A supply chain network equilibrium model with random demands," European Journal of Operational Research, Elsevier, vol. 156(1), pages 194-212, July.
    3. Francisco Facchinei & Christian Kanzow, 2010. "Generalized Nash Equilibrium Problems," Annals of Operations Research, Springer, vol. 175(1), pages 177-211, March.
    4. Miller, Naomi & Ruszczynski, Andrzej, 2008. "Risk-adjusted probability measures in portfolio optimization with coherent measures of risk," European Journal of Operational Research, Elsevier, vol. 191(1), pages 193-206, November.
    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. 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.

    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. 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.
    2. 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.
    3. Longfei He & Qinxu Gu & Junsong Bian & Kin Keung Lai & Xiao Zhang, 2023. "To Pool or Not to Pool in Carbon Quotas: Analyses of Emission Regulation and Operations in Supply Chain Supernetwork under Cap-and-Trade Policy," Annals of Operations Research, Springer, vol. 324(1), pages 311-353, May.
    4. Oliver Stein & Nathan Sudermann-Merx, 2016. "The Cone Condition and Nonsmoothness in Linear Generalized Nash Games," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 687-709, August.
    5. Nadja Harms & Tim Hoheisel & Christian Kanzow, 2015. "On a Smooth Dual Gap Function for a Class of Player Convex Generalized Nash Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 659-685, August.
    6. Balbás, Alejandro & Balbás, Beatriz & Heras, Antonio, 2011. "Stable solutions for optimal reinsurance problems involving risk measures," European Journal of Operational Research, Elsevier, vol. 214(3), pages 796-804, November.
    7. Lorenzo Lampariello & Simone Sagratella, 2015. "It is a matter of hierarchy: a Nash equilibrium problem perspective on bilevel programming," DIAG Technical Reports 2015-07, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    8. Lizyayev, Andrey & Ruszczyński, Andrzej, 2012. "Tractable Almost Stochastic Dominance," European Journal of Operational Research, Elsevier, vol. 218(2), pages 448-455.
    9. Carland, Corinne & Goentzel, Jarrod & Montibeller, Gilberto, 2018. "Modeling the values of private sector agents in multi-echelon humanitarian supply chains," European Journal of Operational Research, Elsevier, vol. 269(2), pages 532-543.
    10. Borgonovo, Emanuele & Gatti, Stefano, 2013. "Risk analysis with contractual default. Does covenant breach matter?," European Journal of Operational Research, Elsevier, vol. 230(2), pages 431-443.
    11. Constantin Zopounidis & Michael Doumpos, 2013. "Rejoinder on: Multicriteria decision systems for financial problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 282-286, July.
    12. Alexey Izmailov & Mikhail Solodov, 2014. "On error bounds and Newton-type methods for generalized Nash equilibrium problems," Computational Optimization and Applications, Springer, vol. 59(1), pages 201-218, October.
    13. Leonardo Galli & Christian Kanzow & Marco Sciandrone, 2018. "A nonmonotone trust-region method for generalized Nash equilibrium and related problems with strong convergence properties," Computational Optimization and Applications, Springer, vol. 69(3), pages 629-652, April.
    14. Nagurney, Anna, 2021. "Supply chain game theory network modeling under labor constraints: Applications to the Covid-19 pandemic," European Journal of Operational Research, Elsevier, vol. 293(3), pages 880-891.
    15. Otgochuluu, Ch. & Altangerel, L. & Battur, G. & Khashchuluun, Ch. & Dorjsundui, G., 2021. "A game theory application in the copper market," Resources Policy, Elsevier, vol. 70(C).
    16. 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.
    17. Denizalp Goktas & Jiayi Zhao & Amy Greenwald, 2023. "T\^atonnement in Homothetic Fisher Markets," Papers 2306.04890, arXiv.org.
    18. Simone Sagratella, 2017. "Algorithms for generalized potential games with mixed-integer variables," Computational Optimization and Applications, Springer, vol. 68(3), pages 689-717, December.
    19. Tatsuya Hirano & Yasushi Narushima, 2019. "Robust Supply Chain Network Equilibrium Model," Transportation Science, INFORMS, vol. 53(4), pages 1196-1212, July.
    20. Amir Gandomi & Amirhossein Bazargan & Saeed Zolfaghari, 2019. "Designing competitive loyalty programs: a stochastic game-theoretic model to guide the choice of reward structure," Annals of Operations Research, Springer, vol. 280(1), pages 267-298, 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:indpam:v:50:y:2019:i:4:d:10.1007_s13226-019-0363-2. 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.