IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v145y2010i2d10.1007_s10957-009-9644-y.html
   My bibliography  Save this article

Existence and Boundedness of the Kuhn-Tucker Multipliers in Nonsmooth Multiobjective Optimization

Author

Listed:
  • X. F. Li

    (Jilin University)

  • J. Z. Zhang

    (BJNU-HKBU United International College)

Abstract

Using the idea of upper convexificators, we propose constraint qualifications and study existence and boundedness of the Kuhn-Tucker multipliers for a nonsmooth multiobjective optimization problem with inequality constraints and an arbitrary set constraint. We show that, at locally weak efficient solutions where the objective and constraint functions are locally Lipschitz, the constraint qualifications are necessary and sufficient conditions for the Kuhn-Tucker multiplier sets to be nonempty and bounded under certain semiregularity assumptions on the upper convexificators of the functions.

Suggested Citation

  • X. F. Li & J. Z. Zhang, 2010. "Existence and Boundedness of the Kuhn-Tucker Multipliers in Nonsmooth Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 373-386, May.
    • Handle: RePEc:spr:joptap:v:145:y:2010:i:2:d:10.1007_s10957-009-9644-y
    DOI: 10.1007/s10957-009-9644-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-009-9644-y
    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/s10957-009-9644-y?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. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1157-1160, December.
    2. V. Jeyakumar & D. T. Luc, 1999. "Nonsmooth Calculus, Minimality, and Monotonicity of Convexificators," Journal of Optimization Theory and Applications, Springer, vol. 101(3), pages 599-621, June.
    3. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
    4. J. Dutta & S. Chandra, 2002. "Convexifactors, Generalized Convexity, and Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 113(1), pages 41-64, April.
    5. D. E. Ward & G. M. Lee, 2001. "Generalized properly efficient solutions of vector optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 53(2), pages 215-232, June.
    6. X. F. Li & J. Z. Zhang, 2005. "Stronger Kuhn-Tucker Type Conditions in Nonsmooth Multiobjective Optimization: Locally Lipschitz Case," Journal of Optimization Theory and Applications, Springer, vol. 127(2), pages 367-388, 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. Thai Doan Chuong, 2020. "Optimality conditions for nonsmooth multiobjective bilevel optimization problems," Annals of Operations Research, Springer, vol. 287(2), pages 617-642, April.
    2. Alireza Kabgani & Majid Soleimani-damaneh & Moslem Zamani, 2017. "Optimality conditions in optimization problems with convex feasible set using convexificators," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(1), pages 103-121, August.

    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. X. F. Li & J. Z. Zhang, 2006. "Necessary Optimality Conditions in Terms of Convexificators in Lipschitz Optimization," Journal of Optimization Theory and Applications, Springer, vol. 131(3), pages 429-452, December.
    2. World Bank, 2002. "Costa Rica : Social Spending and the Poor, Volume 1. Summary of Issues and Recommendations with Executive Summary," World Bank Publications - Reports 15330, The World Bank Group.
    3. Hernández-Hernández, M.E. & Kolokoltsov, V.N. & Toniazzi, L., 2017. "Generalised fractional evolution equations of Caputo type," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 184-196.
    4. Simon Levin & Anastasios Xepapadeas, 2021. "On the Coevolution of Economic and Ecological Systems," Annual Review of Resource Economics, Annual Reviews, vol. 13(1), pages 355-377, October.
    5. Hoang Ngoc Tuan, 2015. "Boundedness of a Type of Iterative Sequences in Two-Dimensional Quadratic Programming," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 234-245, January.
    6. Wang, Daojuan & Hain, Daniel S. & Larimo, Jorma & Dao, Li T., 2020. "Cultural differences and synergy realization in cross-border acquisitions," International Business Review, Elsevier, vol. 29(3).
    7. Zhou, H. & Uhlaner, L.M., 2009. "Knowledge Management in the SME and its Relationship to Strategy, Family Orientation and Organization Learning," ERIM Report Series Research in Management ERS-2009-026-ORG, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    8. Turpie, J.K. & Marais, C. & Blignaut, J.N., 2008. "The working for water programme: Evolution of a payments for ecosystem services mechanism that addresses both poverty and ecosystem service delivery in South Africa," Ecological Economics, Elsevier, vol. 65(4), pages 788-798, May.
    9. Koichi Hamada & Asahi Noguchi, 2005. "The Role of Preconceived Ideas in Macroeconomic Policy: Japan's Experiences in the Two Deflationary Periods," Working Papers 908, Economic Growth Center, Yale University.
    10. Jingyi Xue, 2018. "Fair division with uncertain needs," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(1), pages 105-136, June.
    11. Dipak R. Pant, 2013. "Managing the global waste in the 21st century: As an anthropologist views it," LIUC Papers in Economics 263, Cattaneo University (LIUC).
    12. van der Laan, Gerard & Talman, Dolf & Yang, Zaifu, 2011. "Solving discrete systems of nonlinear equations," European Journal of Operational Research, Elsevier, vol. 214(3), pages 493-500, November.
    13. Richard ANKER, 2006. "Poverty lines around the world: A new methodology and internationally comparable estimates," International Labour Review, International Labour Organization, vol. 145(4), pages 279-307, December.
    14. Popli, Manish & Akbar, Mohammad & Kumar, Vikas & Gaur, Ajai, 2016. "Reconceptualizing cultural distance: The role of cultural experience reserve in cross-border acquisitions," Journal of World Business, Elsevier, vol. 51(3), pages 404-412.
    15. A. Kabgani & F. Lara, 2023. "Semistrictly and neatly quasiconvex programming using lower global subdifferentials," Journal of Global Optimization, Springer, vol. 86(4), pages 845-865, August.
    16. Alireza Kabgani, 2021. "Characterization of Nonsmooth Quasiconvex Functions and their Greenberg–Pierskalla’s Subdifferentials Using Semi-Quasidifferentiability notion," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 666-678, May.
    17. Quah Chee-Heong, 2019. "China’s Dollar-linked Hong Kong during the Global Crisis," Apuntes del Cenes, Universidad Pedagógica y Tecnológica de Colombia, vol. 38(67), pages 95-121, February.
    18. Lan, Heng-you, 2021. "Approximation-solvability of population biology systems based on p-Laplacian elliptic inequalities with demicontinuous strongly pseudo-contractive operators," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    19. Teresa Estañ & Natividad Llorca & Ricardo Martínez & Joaquín Sánchez-Soriano, 2020. "On the difficulty of budget allocation in claims problems with indivisible items of different prices," ThE Papers 20/09, Department of Economic Theory and Economic History of the University of Granada..
    20. Slotnick, Susan A., 2011. "Order acceptance and scheduling: A taxonomy and review," European Journal of Operational Research, Elsevier, vol. 212(1), pages 1-11, 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:joptap:v:145:y:2010:i:2:d:10.1007_s10957-009-9644-y. 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.