IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v54y2012i3p537-549.html
   My bibliography  Save this article

Second order sufficient optimality conditions in vector optimization

Author

Listed:
  • Ning E.
  • Wen Song
  • Yu Zhang

Abstract

In this paper, we mainly consider second-order sufficient conditions for vector optimization problems. We first present a second-order sufficient condition for isolated local minima of order 2 to vector optimization problems and then prove that the second-order sufficient condition can be simplified in the case where the constrained cone is a convex generalized polyhedral and/or Robinson’s constraint qualification holds. Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:54:y:2012:i:3:p:537-549
    DOI: 10.1007/s10898-011-9776-0
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-011-9776-0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-011-9776-0?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. J. B. Hiriart-Urruty, 1979. "Tangent Cones, Generalized Gradients and Mathematical Programming in Banach Spaces," Mathematics of Operations Research, INFORMS, vol. 4(1), pages 79-97, February.
    3. Giancarlo Bigi, 2006. "On sufficient second order optimality conditions in multiobjective optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(1), pages 77-85, 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. Mohammad Taghi Nadi & Jafar Zafarani, 2023. "Second-order characterization of convex mappings in Banach spaces and its applications," Journal of Global Optimization, Springer, vol. 86(4), pages 1005-1023, August.
    2. Yi-Hong Xu & Zhen-Hua Peng, 2018. "Second-Order M-Composed Tangent Derivative and Its Applications," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(05), pages 1-20, October.
    3. 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.
    4. 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.
    5. 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.
    6. Nguyen Thi Toan & Le Quang Thuy & Nguyen Tuyen & Yi-Bin Xiao, 2021. "Second-order KKT optimality conditions for multiobjective discrete optimal control problems," Journal of Global Optimization, Springer, vol. 79(1), pages 203-231, January.

    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. 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.
    2. 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.
    3. Marius Durea & Radu Strugariu & Christiane Tammer, 2013. "Scalarization in Geometric and Functional Vector Optimization Revisited," Journal of Optimization Theory and Applications, Springer, vol. 159(3), pages 635-655, December.
    4. Thai Chuong, 2013. "Newton-like methods for efficient solutions in vector optimization," Computational Optimization and Applications, Springer, vol. 54(3), pages 495-516, April.
    5. 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.
    6. 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.
    7. P. Q. Khanh & N. D. Tuan, 2007. "Optimality Conditions for Nonsmooth Multiobjective Optimization Using Hadamard Directional Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 341-357, June.
    8. Bolte, Jérôme & Le, Tam & Pauwels, Edouard & Silveti-Falls, Antonio, 2022. "Nonsmooth Implicit Differentiation for Machine Learning and Optimization," TSE Working Papers 22-1314, Toulouse School of Economics (TSE).
    9. Khushboo & C. S. Lalitha, 2018. "Scalarizations for a unified vector optimization problem based on order representing and order preserving properties," Journal of Global Optimization, Springer, vol. 70(4), pages 903-916, April.
    10. Ginchev Ivan & Guerraggio Angelo & Rocca Matteo, 2003. "First-Order Conditions for C0,1 Constrained vector optimization," Economics and Quantitative Methods qf0307, Department of Economics, University of Insubria.
    11. Yang-Dong Xu & Cheng-Ling Zhou & Sheng-Kun Zhu, 2021. "Image Space Analysis for Set Optimization Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 311-343, October.
    12. María C. Maciel & Sandra A. Santos & Graciela N. Sottosanto, 2021. "On Second-Order Optimality Conditions for Vector Optimization: Addendum," Journal of Optimization Theory and Applications, Springer, vol. 188(2), pages 597-602, February.
    13. Hong-Zhi Wei & Chun-Rong Chen & Sheng-Jie Li, 2020. "Robustness Characterizations for Uncertain Optimization Problems via Image Space Analysis," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 459-479, August.
    14. M. J. Cánovas & M. A. López & J. Parra & F. J. Toledo, 2006. "Distance to Ill-Posedness in Linear Optimization via the Fenchel-Legendre Conjugate," Journal of Optimization Theory and Applications, Springer, vol. 130(2), pages 173-183, August.
    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. S. K. Zhu & S. J. Li, 2014. "Unified Duality Theory for Constrained Extremum Problems. Part II: Special Duality Schemes," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 763-782, June.
    17. Qamrul Hasan Ansari & Pradeep Kumar Sharma, 2022. "Some Properties of Generalized Oriented Distance Function and their Applications to Set Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 247-279, June.
    18. 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.
    19. Onetti Alberto & Verma Sameer, 2008. "Licensing and Business Models," Economics and Quantitative Methods qf0806, Department of Economics, University of Insubria.
    20. Elisa Caprari & Lorenzo Cerboni Baiardi & Elena Molho, 2022. "Scalarization and robustness in uncertain vector optimization problems: a non componentwise approach," Journal of Global Optimization, Springer, vol. 84(2), pages 295-320, October.

    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:54:y:2012:i:3:p:537-549. 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.