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Second-Order Optimality Conditions for Vector Problems with Continuously Fréchet Differentiable Data and Second-Order Constraint Qualifications

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  • Vsevolod I. Ivanov

    (Technical University of Varna)

Abstract

In the present paper, we consider the inequality constrained vector problem with continuously Fréchet differentiable objective functions and constraints. We obtain second-order necessary optimality conditions of Karush–Kuhn–Tucker type for weak efficiency. A new second-order constraint qualification of Zangwill type is introduced. It is applied in the optimality conditions. Some connections with other constraint qualifications are established.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:166:y:2015:i:3:d:10.1007_s10957-015-0718-8
    DOI: 10.1007/s10957-015-0718-8
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    References listed on IDEAS

    as
    1. T. Maeda, 2004. "Second-Order Conditions for Efficiency in Nonsmooth Multiobjective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 122(3), pages 521-538, 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.
    3. 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.
    4. Ivan Ginchev & Vsevolod I. Ivanov, 2007. "Higher-order Pseudoconvex Functions," Lecture Notes in Economics and Mathematical Systems, in: Generalized Convexity and Related Topics, pages 247-264, Springer.
    5. 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.
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    Citations

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    Cited by:

    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. 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.
    3. Min Feng & Shengjie Li, 2019. "Second-Order Strong Karush/Kuhn–Tucker Conditions for Proper Efficiencies in Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 766-786, June.

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    More about this item

    Keywords

    Vector optimization; Second-order KKT optimality conditions; Second-order constraint qualifications; Nonsmooth optimization; C1 problems with inequality constraints;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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