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New Results on Second-Order Optimality Conditions in Vector Optimization Problems

Author

Listed:
  • M. Hachimi

    (Universié Ibn Zohr)

  • B. Aghezzaf

    (Université Hassan II Aïn chock)

Abstract

In this paper, we study second-order optimality conditions for multiobjective optimization problems. By means of different second-order tangent sets, various new second-order necessary optimality conditions are obtained in both scalar and vector optimization. As special cases, we obtain several results found in the literature (see reference list). We present also second-order sufficient optimality conditions so that there is only a very small gap with the necessary optimality conditions.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:135:y:2007:i:1:d:10.1007_s10957-007-9242-9
    DOI: 10.1007/s10957-007-9242-9
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    References listed on IDEAS

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    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. 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.
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    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. Elena Constantin, 2019. "Necessary conditions for weak efficiency for nonsmooth degenerate multiobjective optimization problems," Journal of Global Optimization, Springer, vol. 75(1), pages 111-129, September.
    5. 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.

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