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On Second-Order Optimality Conditions for Vector Optimization

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Abstract

In this article, two second-order constraint qualifications for the vector optimization problem are introduced, that come from first-order constraint qualifications, originally devised for the scalar case. The first is based on the classical feasible arc constraint qualification, proposed by Kuhn and Tucker (Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 481–492, University of California Press, California, 1951) together with a slight modification of McCormick’s second-order constraint qualification. The second—the constant rank constraint qualification—was introduced by Janin (Math. Program. Stud. 21:110–126, 1984). They are used to establish two second-order necessary conditions for the vector optimization problem, with general nonlinear constraints, without any convexity assumption.

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Authors and Affiliations

  1. Department of Mathematics, Southern National University, Av. Alem 1253, 8000, Bahía Blanca, Argentina

    María C. Maciel

  2. Department of Applied Mathematics, State University of Campinas, 13083-970, Campinas, SP, Brazil

    Sandra A. Santos

  3. Department of Mathematics, Comahue National University, Santa Fe 1400, 8300, Neuquén, Argentina

    Graciela N. Sottosanto

Authors
  1. María C. Maciel
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  2. Sandra A. Santos
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  3. Graciela N. Sottosanto
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Corresponding author

Correspondence to Sandra A. Santos.

Additional information

This work was partially supported by Southern National University (Grant UNS 24/L069), Comahue National University (Grant E081/09), CNPq (Grants 303465/2007-7 and 304032/2010-7), FAPESP (Grant 2006-53768-0) and PRONEX-Optimization. The authors are grateful for the valuable suggestions of the referees, which helped to improve the original presentation of the manuscript.

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Maciel, M.C., Santos, S.A. & Sottosanto, G.N. On Second-Order Optimality Conditions for Vector Optimization. J Optim Theory Appl 149, 332–351 (2011). https://doi.org/10.1007/s10957-010-9793-z

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