IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2011y2011i1n432963.html

Second‐Order Optimality Conditions for Set‐Valued Optimization Problems Under Benson Proper Efficiency

Author

Listed:
  • Qilin Wang
  • Guolin Yu

Abstract

Some new properties are obtained for generalized second‐order contingent (adjacent) epiderivatives of set‐valued maps. By employing the generalized second‐order adjacent epiderivatives, necessary and sufficient conditions of Benson proper efficient solutions are given for set‐valued optimization problems. The results obtained improve the corresponding results in the literature.

Suggested Citation

  • Qilin Wang & Guolin Yu, 2011. "Second‐Order Optimality Conditions for Set‐Valued Optimization Problems Under Benson Proper Efficiency," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    • Handle: RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:432963
    DOI: 10.1155/2011/432963
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2011/432963
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2011/432963?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
    ---><---

    References listed on IDEAS

    as
    1. Guang Ya Chen & Johannes Jahn, 1998. "Optimality conditions for set-valued optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 187-200, November.
    2. G. Y. Chen & W. D. Rong, 1998. "Characterizations of the Benson Proper Efficiency for Nonconvex Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 365-384, August.
    3. 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.
    4. Johannes Jahn & Rüdiger Rauh, 1997. "Contingent epiderivatives and set-valued optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(2), pages 193-211, 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. 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.
    2. Qilin Wang & Guolin Yu, 2012. "Higher‐Order Weakly Generalized Epiderivatives and Applications to Optimality Conditions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. P. Q. Khanh & N. D. Tuan, 2008. "Variational Sets of Multivalued Mappings and a Unified Study of Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 47-65, October.
    4. Xiang-Kai Sun & Sheng-Jie Li, 2014. "Generalized second-order contingent epiderivatives in parametric vector optimization problems," Journal of Global Optimization, Springer, vol. 58(2), pages 351-363, February.
    5. 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.
    6. Nguyen Thi Toan & Le Quang Thuy, 2023. "S-Derivative of the Extremum Multifunction to a Multi-objective Parametric Discrete Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 240-265, January.
    7. Elvira Hernández & Luis Rodríguez-Marín, 2011. "Weak and Strong Subgradients of Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 149(2), pages 352-365, May.
    8. Nguyen Anh & Phan Khanh, 2013. "Higher-order optimality conditions in set-valued optimization using radial sets and radial derivatives," Journal of Global Optimization, Springer, vol. 56(2), pages 519-536, June.
    9. T. D. Chuong & J. C. Yao, 2010. "Generalized Clarke Epiderivatives of Parametric Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 77-94, July.
    10. Koushik Das & Chandal Nahak, 2026. "Sufficiency and duality for set-valued optimization problems with $$\kappa$$ κ -cone arcwise connectedness of higher-order," OPSEARCH, Springer;Operational Research Society of India, vol. 63(1), pages 104-128, March.
    11. S. J. Li & S. K. Zhu & K. L. Teo, 2012. "New Generalized Second-Order Contingent Epiderivatives and Set-Valued Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 587-604, March.
    12. Liu He & Qi-Lin Wang & Ching-Feng Wen & Xiao-Yan Zhang & Xiao-Bing Li, 2019. "A Kind of New Higher-Order Mond-Weir Type Duality for Set-Valued Optimization Problems," Mathematics, MDPI, vol. 7(4), pages 1-18, April.
    13. S. Zhu & S. Li & K. Teo, 2014. "Second-order Karush–Kuhn–Tucker optimality conditions for set-valued optimization," Journal of Global Optimization, Springer, vol. 58(4), pages 673-692, April.
    14. J. Baier & J. Jahn, 1999. "On Subdifferentials of Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 100(1), pages 233-240, January.
    15. J. Y. Bello Cruz & G. Bouza Allende, 2014. "A Steepest Descent-Like Method for Variable Order Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 371-391, August.
    16. Davide LA TORRE, 2004. "Characterizations of convex vector functions and optimization by mollified derivatives," Departmental Working Papers 2004-09, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    17. X. L. Guo & S. J. Li, 2014. "Optimality Conditions for Vector Optimization Problems with Difference of Convex Maps," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 821-844, September.
    18. Tran Van Su, 2023. "Optimality and duality for nonsmooth mathematical programming problems with equilibrium constraints," Journal of Global Optimization, Springer, vol. 85(3), pages 663-685, March.
    19. Tran Su & Dinh Dieu Hang, 2022. "Optimality and duality in nonsmooth multiobjective fractional programming problem with constraints," 4OR, Springer, vol. 20(1), pages 105-137, March.
    20. Abadir, Karim, 1995. "On Efficient Simulations in Dynamic Models," Discussion Papers 9521, University of Exeter, Department of Economics.

    More about this item

    Statistics

    Access and download statistics

    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:wly:jnlaaa:v:2011:y:2011:i:1:n:432963. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    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.