IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v60y2014i4p679-688.html
   My bibliography  Save this article

Existence theorem for a class of generalized quasi-variational inequalities

Author

Listed:
  • Monica Milasi

Abstract

In this paper we consider a class of generalized quasi-variational inequalities. The variational problem is studied in the convex set $$X\times Y$$ X × Y , with $$Y$$ Y bounded and $$X$$ X unbounded. In the latter settings, we investigate about the solvability of the problem. In particular, by using the perturbation theory, we give an existence result of the solution without requesting any coercivity hypothesis on the operator. Finally, we give an application to the obtained theoretical results in terms of an economic equilibrium problem. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Monica Milasi, 2014. "Existence theorem for a class of generalized quasi-variational inequalities," Journal of Global Optimization, Springer, vol. 60(4), pages 679-688, December.
    • Handle: RePEc:spr:jglopt:v:60:y:2014:i:4:p:679-688
    DOI: 10.1007/s10898-013-0114-6
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-013-0114-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-013-0114-6?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. G. Anello & M. Donato & M. Milasi, 2010. "A quasi-variational approach to a competitive economic equilibrium problem without strong monotonicity assumption," Journal of Global Optimization, Springer, vol. 48(2), pages 279-287, October.
    2. D. Chan & J. S. Pang, 1982. "The Generalized Quasi-Variational Inequality Problem," Mathematics of Operations Research, INFORMS, vol. 7(2), pages 211-222, May.
    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. Monica Milasi & Domenico Scopelliti, 2021. "A Variational Approach to the Maximization of Preferences Without Numerical Representation," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 879-893, September.
    2. Sonia & Ratna Dev Sarma, 2023. "A topological approach for vector quasi-variational inequalities with set-valued functions," Computational Management Science, Springer, vol. 20(1), pages 1-13, December.

    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. Maria Bernadette Donato & Monica Milasi & Carmela Vitanza, 2016. "On the Study of an Economic Equilibrium with Variational Inequality Arguments," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 646-660, February.
    2. Flam, Sjur & Ruszczynski, A., 2006. "Computing Normalized Equilibria in Convex-Concave Games," Working Papers 2006:9, Lund University, Department of Economics.
    3. Tian, Guoqiang, 1991. "Generalized quasi-variational-like inequality problem," MPRA Paper 41219, University Library of Munich, Germany, revised 26 May 1992.
    4. Jacqueline Boucher & Yves Smeers, 2001. "Alternative Models of Restructured Electricity Systems, Part 1: No Market Power," Operations Research, INFORMS, vol. 49(6), pages 821-838, December.
    5. N. Minh & N. Tan, 2006. "On the Existence of Solutions of Quasi-equilibrium Problems with Constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(1), pages 17-31, August.
    6. Francisco Facchinei & Christian Kanzow, 2010. "Generalized Nash Equilibrium Problems," Annals of Operations Research, Springer, vol. 175(1), pages 177-211, March.
    7. 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.
    8. Ankur A. Kulkarni & Uday V. Shanbhag, 2012. "Revisiting Generalized Nash Games and Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 175-186, July.
    9. Paolo Cubiotti & Jen-Chih Yao, 1997. "Discontinuous implicit quasi-variational inequalities with applications to fuzzy mappings," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(2), pages 213-228, June.
    10. Giancarlo Bigi & Mauro Passacantando, 2016. "Gap functions for quasi-equilibria," Journal of Global Optimization, Springer, vol. 66(4), pages 791-810, December.
    11. P. Cubiotti, 1997. "Generalized Quasi-Variational Inequalities Without Continuities," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 477-495, March.
    12. Zhou, Jing & Lam, William H.K. & Heydecker, Benjamin G., 2005. "The generalized Nash equilibrium model for oligopolistic transit market with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 39(6), pages 519-544, July.
    13. Laura Scrimali, 2012. "Infinite Dimensional Duality Theory Applied to Investment Strategies in Environmental Policy," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 258-277, July.
    14. L. F. Bueno & G. Haeser & F. Lara & F. N. Rojas, 2020. "An Augmented Lagrangian method for quasi-equilibrium problems," Computational Optimization and Applications, Springer, vol. 76(3), pages 737-766, July.
    15. SCRIMALI, Laura, 2006. "A quasi-variational inequality approach to the financial equilibrium problem," LIDAM Discussion Papers CORE 2006108, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    16. Igor Konnov, 2021. "Variational Inequality Type Formulations of General Market Equilibrium Problems with Local Information," Journal of Optimization Theory and Applications, Springer, vol. 188(2), pages 332-355, February.
    17. Marco Castellani & Massimiliano Giuli & Sara Latini, 2023. "Projected solutions for finite-dimensional quasiequilibrium problems," Computational Management Science, Springer, vol. 20(1), pages 1-14, December.
    18. P. Cubiotti, 1997. "Generalized Quasi-Variational Inequalities in Infinite-Dimensional Normed Spaces," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 457-475, March.
    19. Nadja Harms & Tim Hoheisel & Christian Kanzow, 2014. "On a Smooth Dual Gap Function for a Class of Quasi-Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 413-438, November.
    20. S. X. Li, 1998. "Cone Concavity and Multiple-Payoff Constrained n-Person Games," Journal of Optimization Theory and Applications, Springer, vol. 97(1), pages 119-149, 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:60:y:2014:i:4:p:679-688. 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.