IDEAS home Printed from https://ideas.repec.org/a/spr/aqjoor/v16y2018i2d10.1007_s10288-017-0360-4.html
   My bibliography  Save this article

New optimality conditions for unconstrained vector equilibrium problem in terms of contingent derivatives in Banach spaces

Author

Listed:
  • Tran Van Su

    (Quangnam University
    Graduate University of Science and Technology, Vietnam Academy of Science and Technology)

Abstract

This article presents necessary and sufficient optimality conditions for weakly efficient solution, Henig efficient solution, globally efficient solution and superefficient solution of vector equilibrium problem without constraints in terms of contingent derivatives in Banach spaces with stable functions. Using the steadiness and stability on a neighborhood of optimal point, necessary optimality conditions for efficient solutions are derived. Under suitable assumptions on generalized convexity, sufficient optimality conditions are established. Without assumptions on generalized convexity, a necessary and sufficient optimality condition for efficient solutions of unconstrained vector equilibrium problem is also given. Many examples to illustrate for the obtained results in the paper are derived as well.

Suggested Citation

  • Tran Van Su, 2018. "New optimality conditions for unconstrained vector equilibrium problem in terms of contingent derivatives in Banach spaces," 4OR, Springer, vol. 16(2), pages 173-198, June.
    • Handle: RePEc:spr:aqjoor:v:16:y:2018:i:2:d:10.1007_s10288-017-0360-4
    DOI: 10.1007/s10288-017-0360-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10288-017-0360-4
    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/s10288-017-0360-4?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. Do Luu, 2016. "Optimality Condition for Local Efficient Solutions of Vector Equilibrium Problems via Convexificators and Applications," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 643-665, November.
    2. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(1), pages 193-194, February.
    3. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(2), pages 541-545, April.
    4. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(4), pages 1007-1017, August.
    5. X. H. Gong, 2001. "Efficiency and Henig Efficiency for Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 108(1), pages 139-154, January.
    6. Q.H. Ansari & I.V. Konnov & J.C. Yao, 2002. "Characterizations of Solutions for Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 113(3), pages 435-447, June.
    7. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1461-1465, December.
    8. Q. H. Ansari & I. V. Konnov & J. C. Yao, 2001. "Existence of a Solution and Variational Principles for Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 110(3), pages 481-492, September.
    9. Do Luu & Dinh Hang, 2014. "Efficient solutions and optimality conditions for vector equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(2), pages 163-177, April.
    10. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1273-1289, October.
    11. M. Bianchi & N. Hadjisavvas & S. Schaible, 1997. "Vector Equilibrium Problems with Generalized Monotone Bifunctions," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 527-542, March.
    12. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(3), pages 819-821, June.
    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. Adela Capătă, 2011. "Existence results for proper efficient solutions of vector equilibrium problems and applications," Journal of Global Optimization, Springer, vol. 51(4), pages 657-675, December.
    2. Szilárd László, 2016. "Vector Equilibrium Problems on Dense Sets," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 437-457, August.
    3. Ouayl Chadli & Qamrul Hasan Ansari & Suliman Al-Homidan, 2017. "Existence of Solutions and Algorithms for Bilevel Vector Equilibrium Problems: An Auxiliary Principle Technique," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 726-758, March.
    4. J. Y. Fu, 2006. "Stampacchia Generalized Vector Quasiequilibrium Problems and Vector Saddle Points," Journal of Optimization Theory and Applications, Springer, vol. 128(3), pages 605-619, March.
    5. Wensheng Jia & Xiaoling Qiu & Dingtao Peng, 2020. "An Approximation Theorem for Vector Equilibrium Problems under Bounded Rationality," Mathematics, MDPI, vol. 8(1), pages 1-9, January.
    6. Li, S.J. & Chen, C.R. & Wu, S.Y., 2009. "Conjugate dual problems in constrained set-valued optimization and applications," European Journal of Operational Research, Elsevier, vol. 196(1), pages 21-32, July.
    7. J. Y. Fu & S. H. Wang & Z. D. Huang, 2007. "New Type of Generalized Vector Quasiequilibrium Problem," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 643-652, December.
    8. César Gutiérrez & Rubén López, 2020. "On the Existence of Weak Efficient Solutions of Nonconvex Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 880-902, June.
    9. Fabián Flores-Bazán & Elvira Hernández, 2013. "Optimality conditions for a unified vector optimization problem with not necessarily preordering relations," Journal of Global Optimization, Springer, vol. 56(2), pages 299-315, June.
    10. Nguyen Hai & Phan Khanh & Nguyen Quan, 2009. "On the existence of solutions to quasivariational inclusion problems," Computational Optimization and Applications, Springer, vol. 45(4), pages 565-581, December.
    11. F. Flores-Bazán & C. Vera, 2006. "Characterization of the Nonemptiness and Compactness of Solution Sets in Convex and Nonconvex Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 130(2), pages 185-207, August.
    12. Claudia García-García & Catalina B. García-García & Román Salmerón, 2021. "Confronting collinearity in environmental regression models: evidence from world data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 895-926, September.
    13. Cambier, Adrien & Chardy, Matthieu & Figueiredo, Rosa & Ouorou, Adam & Poss, Michael, 2022. "Optimizing subscriber migrations for a telecommunication operator in uncertain context," European Journal of Operational Research, Elsevier, vol. 298(1), pages 308-321.
    14. Libura, Marek, 2007. "On the adjustment problem for linear programs," European Journal of Operational Research, Elsevier, vol. 183(1), pages 125-134, November.
    15. Christophe Loussouarn & Carine Franc & Yann Videau & Julien Mousquès, 2021. "Can General Practitioners Be More Productive? The Impact of Teamwork and Cooperation with Nurses on GP Activities," Health Economics, John Wiley & Sons, Ltd., vol. 30(3), pages 680-698, March.
    16. Tschakert, Petra, 2016. "Shifting Discourses of Vilification and the Taming of Unruly Mining Landscapes in Ghana," World Development, Elsevier, vol. 86(C), pages 123-132.
    17. María-Consuelo Casabán & Rafael Company & Lucas Jódar, 2020. "Non-Gaussian Quadrature Integral Transform Solution of Parabolic Models with a Finite Degree of Randomness," Mathematics, MDPI, vol. 8(7), pages 1-16, July.
    18. Isabelle Boutron & Peter John & David J. Torgerson, 2010. "Reporting Methodological Items in Randomized Experiments in Political Science," The ANNALS of the American Academy of Political and Social Science, , vol. 628(1), pages 112-131, March.
    19. Ben Slimane, Faten & Padilla Angulo, Laura, 2019. "Strategic change and corporate governance: Evidence from the stock exchange industry," Journal of Business Research, Elsevier, vol. 103(C), pages 206-218.
    20. Bossert, Walter & Derks, Jean & Peters, Hans, 2005. "Efficiency in uncertain cooperative games," Mathematical Social Sciences, Elsevier, vol. 50(1), pages 12-23, July.

    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:aqjoor:v:16:y:2018:i:2:d:10.1007_s10288-017-0360-4. 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.