IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v70y2018i2d10.1007_s10898-017-0556-3.html
   My bibliography  Save this article

Second-order necessary efficiency conditions for nonsmooth vector equilibrium problems

Author

Listed:
  • Do Van Luu

    (Thang Long University)

Abstract

This paper presents primal and dual second-order Fritz John necessary conditions for weak efficiency of nonsmooth vector equilibrium problems involving inequality, equality and set constraints in terms of the Páles–Zeidan second-order directional derivatives. Dual second-order Karush–Kuhn–Tucker necessary conditions for weak efficiency are established under suitable second-order constraint qualifications.

Suggested Citation

  • Do Van Luu, 2018. "Second-order necessary efficiency conditions for nonsmooth vector equilibrium problems," Journal of Global Optimization, Springer, vol. 70(2), pages 437-453, February.
    • Handle: RePEc:spr:jglopt:v:70:y:2018:i:2:d:10.1007_s10898-017-0556-3
    DOI: 10.1007/s10898-017-0556-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-017-0556-3
    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/s10898-017-0556-3?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. B. Aghezzaf & M. Hachimi, 1999. "Second-Order Optimality Conditions in Multiobjective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 37-50, July.
    2. Do Luu, 2014. "Necessary and Sufficient Conditions for Efficiency Via Convexificators," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 510-526, February.
    3. 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.
    4. Bienvenido Jiménez & Vicente Novo, 2003. "Second order necessary conditions in set constrained differentiable vector optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(2), pages 299-317, November.
    5. J. Morgan & M. Romaniello, 2006. "Scalarization and Kuhn-Tucker-Like Conditions for Weak Vector Generalized Quasivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 130(2), pages 309-316, August.
    6. Patrizia Daniele, 2006. "Dynamic Networks and Evolutionary Variational Inequalities," Books, Edward Elgar Publishing, number 3516.
    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. Elena Constantin, 2019. "Necessary conditions for weak efficiency for nonsmooth degenerate multiobjective optimization problems," Journal of Global Optimization, Springer, vol. 75(1), pages 111-129, September.
    2. Elena Constantin, 2021. "Necessary conditions for weak minima and for strict minima of order two in nonsmooth constrained multiobjective optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 177-193, May.
    3. Elena Constantin, 2020. "Second-Order Optimality Conditions in Locally Lipschitz Inequality-Constrained Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 50-67, July.

    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. 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. S. J. Li & K. L. Teo & X. Q. Yang, 2008. "Higher-Order Optimality Conditions for Set-Valued Optimization," Journal of Optimization Theory and Applications, Springer, vol. 137(3), pages 533-553, June.
    3. María C. Maciel & Sandra A. Santos & Graciela N. Sottosanto, 2011. "On Second-Order Optimality Conditions for Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 149(2), pages 332-351, May.
    4. Giorgio Giorgi, 2019. "Notes on Constraint Qualifications for Second-Order Optimality Conditions," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 11(5), pages 16-32, October.
    5. Giorgio, 2019. "On Second-Order Optimality Conditions in Smooth Nonlinear Programming Problems," DEM Working Papers Series 171, University of Pavia, Department of Economics and Management.
    6. C. Gutiérrez & B. Jiménez & V. Novo, 2009. "New Second-Order Directional Derivative and Optimality Conditions in Scalar and Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 85-106, July.
    7. Anna Nagurney & Qiang Qiang, 2008. "An efficiency measure for dynamic networks modeled as evolutionary variational inequalities with application to the Internet and vulnerability analysis," Netnomics, Springer, vol. 9(1), pages 1-20, January.
    8. Lan Zhao & Jishan Zhu, 2010. "Internet Marketing Budget Allocation: From Practitioner'S Perspective," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 9(05), pages 779-797.
    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. 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.
    11. P. Q. Khanh & N. D. Tuan, 2008. "Higher-Order Variational Sets and Higher-Order Optimality Conditions for Proper Efficiency in Set-Valued Nonsmooth Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 243-261, November.
    12. Patrizia Daniele & Mariagrazia Lorino & Cristina Mirabella, 2016. "The Financial Equilibrium Problem with a Markowitz-Type Memory Term and Adaptive Constraints," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 276-296, October.
    13. Zhaobo Chen & Chunying Tian & Ding Zhang & Dongyan Chen, 2020. "Dynamic model of a supply chain network with sticky price," Operational Research, Springer, vol. 20(2), pages 649-670, June.
    14. J. Jahn & A. A. Khan & P. Zeilinger, 2005. "Second-Order Optimality Conditions in Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 125(2), pages 331-347, May.
    15. A. Guerraggio & D. T. Luc, 2001. "Optimality Conditions for C1,1 Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 615-629, June.
    16. M. Hachimi & B. Aghezzaf, 2007. "New Results on Second-Order Optimality Conditions in Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 135(1), pages 117-133, October.
    17. Patrizia Daniele & Sofia Giuffrè & Mariagrazia Lorino, 2016. "Functional inequalities, regularity and computation of the deficit and surplus variables in the financial equilibrium problem," Journal of Global Optimization, Springer, vol. 65(3), pages 575-596, July.
    18. Balendu Bhooshan Upadhyay & Shubham Kumar Singh & Ioan Stancu-Minasian, 2024. "Constraint Qualifications and Optimality Conditions for Nonsmooth Semidefinite Multiobjective Programming Problems with Mixed Constraints Using Convexificators," Mathematics, MDPI, vol. 12(20), pages 1-21, October.
    19. Ning E. & Wen Song & Yu Zhang, 2012. "Second order sufficient optimality conditions in vector optimization," Journal of Global Optimization, Springer, vol. 54(3), pages 537-549, November.
    20. Bui Trong Kien & Trinh Duy Binh, 2023. "On the second-order optimality conditions for multi-objective optimal control problems with mixed pointwise constraints," Journal of Global Optimization, Springer, vol. 85(1), pages 155-183, January.

    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:70:y:2018:i:2:d:10.1007_s10898-017-0556-3. 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.