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Notes on Constraint Qualifications for Second-Order Optimality Conditions

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  • Giorgio Giorgi

Abstract

In the first part of this paper we point out some basic properties of the critical cones used in second-order optimality conditions and give a simple proof of a strong second-order necessary optimality condition by assuming a “modified” first-order Abadie constraint qualification. In the second part we give some insights on second-order constraint qualifications related to second-order local approximations of the feasible set.

Suggested Citation

  • 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.
    • Handle: RePEc:ibn:jmrjnl:v:11:y:2019:i:5:p:16
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    References listed on IDEAS

    as
    1. Aram Arutyunov & Fernando Lobo Pereira, 2006. "Second-Order Necessary Optimality Conditions for Problems Without A Priori Normality Assumptions," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 1-12, February.
    2. R. Andreani & C. E. Echagüe & M. L. Schuverdt, 2010. "Constant-Rank Condition and Second-Order Constraint Qualification," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 255-266, August.
    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. Nguyen Quang Huy & Nguyen Van Tuyen, 2016. "New Second-Order Optimality Conditions for a Class of Differentiable Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 27-44, October.
    5. Giorgio Giorgi, 2018. "A Guided Tour in Constraint Qualifications for Nonlinear Programming under Differentiability Assumptions," DEM Working Papers Series 160, University of Pavia, Department of Economics and Management.
    6. 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.
    7. Bienvenido Jiménez & Vicente Novo, 2003. "Second order necessary conditions in set constrained differentiable vector optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(2), pages 299-317, November.
    8. A. Baccari, 2004. "On the Classical Necessary Second-Order Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 123(1), pages 213-221, October.
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    More about this item

    Keywords

    second-order necessary optimality conditions; second-order constraint qualifications; second-order tangent sets; Abadie-type conditions;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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