IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v162y2014i2d10.1007_s10957-013-0424-3.html
   My bibliography  Save this article

On Higher-Order Sensitivity Analysis in Nonsmooth Vector Optimization

Author

Listed:
  • H. T. H. Diem

    (College of Cantho)

  • P. Q. Khanh

    (International University of Hochiminh City)

  • L. T. Tung

    (Cantho University)

Abstract

We propose the notion of higher-order radial-contingent derivative of a set-valued map, develop some calculus rules and use them directly to obtain optimality conditions for several particular optimization problems. Then we employ this derivative together with contingent-type derivatives to analyze sensitivity for nonsmooth vector optimization. Properties of higher-order contingent-type derivatives of the perturbation and weak perturbation maps of a parameterized optimization problem are obtained.

Suggested Citation

  • H. T. H. Diem & P. Q. Khanh & L. T. Tung, 2014. "On Higher-Order Sensitivity Analysis in Nonsmooth Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 463-488, August.
  • Handle: RePEc:spr:joptap:v:162:y:2014:i:2:d:10.1007_s10957-013-0424-3
    DOI: 10.1007/s10957-013-0424-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-013-0424-3
    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/s10957-013-0424-3?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. 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.
    2. 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.
    3. N. L. H. Anh & P. Q. Khanh, 2013. "Variational Sets of Perturbation Maps and Applications to Sensitivity Analysis for Constrained Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 363-384, August.
    4. E. K. Makarov & N. N. Rachkovski, 1999. "Unified Representation of Proper Efficiency by Means of Dilating Cones," Journal of Optimization Theory and Applications, Springer, vol. 101(1), pages 141-165, April.
    5. 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.
    6. 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.
    7. A. B. Levy, 2001. "Lipschitzian Multifunctions and a Lipschitzian Inverse Mapping Theorem," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 105-118, February.
    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. Nguyen Xuan Duy Bao & Phan Quoc Khanh & Nguyen Minh Tung, 2022. "Quasi-contingent derivatives and studies of higher-orders in nonsmooth optimization," Journal of Global Optimization, Springer, vol. 84(1), pages 205-228, September.

    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. Nguyen Hoang Anh & Phan Khanh, 2014. "Higher-order optimality conditions for proper efficiency in nonsmooth vector optimization using radial sets and radial derivatives," Journal of Global Optimization, Springer, vol. 58(4), pages 693-709, April.
    2. Nguyen Xuan Duy Bao & Phan Quoc Khanh & Nguyen Minh Tung, 2022. "Quasi-contingent derivatives and studies of higher-orders in nonsmooth optimization," Journal of Global Optimization, Springer, vol. 84(1), pages 205-228, September.
    3. Nguyen Minh Tung & Nguyen Xuan Duy Bao, 2022. "Higher-order set-valued Hadamard directional derivatives: calculus rules and sensitivity analysis of equilibrium problems and generalized equations," Journal of Global Optimization, Springer, vol. 83(2), pages 377-402, June.
    4. N. L. H. Anh & P. Q. Khanh, 2013. "Variational Sets of Perturbation Maps and Applications to Sensitivity Analysis for Constrained Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 363-384, August.
    5. Thai Chuong & Jen-Chih Yao, 2013. "Fréchet subdifferentials of efficient point multifunctions in parametric vector optimization," Journal of Global Optimization, Springer, vol. 57(4), pages 1229-1243, December.
    6. Fernando García-Castaño & Miguel Ángel Melguizo-Padial & G. Parzanese, 2023. "Sublinear scalarizations for proper and approximate proper efficient points in nonconvex vector optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(3), pages 367-382, June.
    7. P. Q. Khanh & N. M. Tung, 2015. "Second-Order Optimality Conditions with the Envelope-Like Effect for Set-Valued Optimization," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 68-90, October.
    8. Thai Doan Chuong & Do Sang Kim, 2014. "Nonsmooth Semi-infinite Multiobjective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 748-762, March.
    9. 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.
    10. F. García & M. A. Melguizo Padial, 2015. "Sensitivity Analysis in Convex Optimization through the Circatangent Derivative," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 420-438, May.
    11. 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.
    12. J. M. Bonnisseau & J. Rivera-Cayupi, 2006. "Constrained Consumptions, Lipschitzian Demands, and Regular Economies," Journal of Optimization Theory and Applications, Springer, vol. 131(2), pages 179-193, November.
    13. Zhenhua Peng & Yihong Xu, 2017. "New Second-Order Tangent Epiderivatives and Applications to Set-Valued Optimization," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 128-140, January.
    14. Khanh, Phan Quoc & Quyen, Ho Thuc & Yao, Jen-Chih, 2011. "Optimality conditions under relaxed quasiconvexity assumptions using star and adjusted subdifferentials," European Journal of Operational Research, Elsevier, vol. 212(2), pages 235-241, July.
    15. Stephen M. Robinson, 2003. "Constraint Nondegeneracy in Variational Analysis," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 201-232, May.
    16. Daniel L. McFadden & Mogens Fosgerau, 2012. "A theory of the perturbed consumer with general budgets," NBER Working Papers 17953, National Bureau of Economic Research, Inc.
    17. Thai Doan Chuong, 2013. "Derivatives of the Efficient Point Multifunction in Parametric Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 247-265, February.
    18. 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.
    19. Nguyen Minh Tung, 2020. "New Higher-Order Strong Karush–Kuhn–Tucker Conditions for Proper Solutions in Nonsmooth Optimization," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 448-475, May.
    20. Thai Doan Chuong & Do Sang Kim, 2018. "Normal regularity for the feasible set of semi-infinite multiobjective optimization problems with applications," Annals of Operations Research, Springer, vol. 267(1), pages 81-99, August.

    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:162:y:2014:i:2:d:10.1007_s10957-013-0424-3. 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.