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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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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.

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Authors and Affiliations

  1. Department of Mathematics, Technical University of Varna, 9010, Varna, Bulgaria

    Vsevolod I. Ivanov

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  1. Vsevolod I. Ivanov
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Correspondence to Vsevolod I. Ivanov.

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Communicated by Fabian Flores-Bazàn.

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Ivanov, V.I. Second-Order Optimality Conditions for Vector Problems with Continuously Fréchet Differentiable Data and Second-Order Constraint Qualifications. J Optim Theory Appl 166, 777–790 (2015). https://doi.org/10.1007/s10957-015-0718-8

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  • DOI: https://doi.org/10.1007/s10957-015-0718-8

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