IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v63y2006i1p77-85.html
   My bibliography  Save this article

On sufficient second order optimality conditions in multiobjective optimization

Author

Listed:
  • Giancarlo Bigi

Abstract

A second order sufficient optimality criterion is presented for a multiobjective problem subject to a constraint given just as a set. To this aim, we first refine known necessary conditions in such a way that the sufficient ones differ by the replacement of inequalities by strict inequalities. Furthermore, we show that no relationship holds between this criterion and a sufficient multipliers rule, when the constraint is described by inequalities and equalities. Finally, improvements of this criterion for the unconstrained case are presented, stressing the differences with single-objective optimization Copyright Springer-Verlag 2006

Suggested Citation

  • 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.
  • Handle: RePEc:spr:mathme:v:63:y:2006:i:1:p:77-85
    DOI: 10.1007/s00186-005-0013-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-005-0013-9
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s00186-005-0013-9?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. S. Bolintinéanu & M. El Maghri, 1998. "Second-Order Efficiency Conditions and Sensitivity of Efficient Points," Journal of Optimization Theory and Applications, Springer, vol. 98(3), pages 569-592, September.
    2. 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.
    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. 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.
    2. 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.
    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. Anulekha Dhara & Aparna Mehra, 2013. "Second-Order Optimality Conditions in Minimax Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 567-590, March.
    5. 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.
    6. 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.
    7. 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.

    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. 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.
    3. A. Guerraggio & D.T. Luc, 2003. "Optimality Conditions for C 1,1 Constrained Multiobjective Problems," Journal of Optimization Theory and Applications, Springer, vol. 116(1), pages 117-129, January.
    4. S. Dempe & N. Gadhi, 2010. "Second order optimality conditions for bilevel set optimization problems," Journal of Global Optimization, Springer, vol. 47(2), pages 233-245, June.
    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. 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.
    8. 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.
    9. Mounir El Maghri & Youssef Elboulqe, 2018. "Reduced Jacobian Method," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 917-943, December.
    10. Mounir El Maghri, 2015. "( $$\epsilon $$ ϵ -)Efficiency in difference vector optimization," Journal of Global Optimization, Springer, vol. 61(4), pages 803-812, April.
    11. 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.
    12. 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.
    13. B. Aghezzaf & M. Hachimi, 2001. "On a Gap between Multiobjective Optimization and Scalar Optimization," Journal of Optimization Theory and Applications, Springer, vol. 109(2), pages 431-435, May.
    14. Vsevolod I. Ivanov, 2015. "Second-Order Optimality Conditions for Vector Problems with Continuously Fréchet Differentiable Data and Second-Order Constraint Qualifications," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 777-790, September.
    15. 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.
    16. Ginchev Ivan & Guerraggio Angelo & Rocca Matteo, 2003. "From scalar to vector optimization," Economics and Quantitative Methods qf0305, Department of Economics, University of Insubria.
    17. 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.
    18. 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.
    19. Bednarczuk, Ewa M., 2004. "Continuity of minimal points with applications to parametric multiple objective optimization," European Journal of Operational Research, Elsevier, vol. 157(1), pages 59-67, 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:mathme:v:63:y:2006:i:1:p:77-85. 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.