On Second-Order Optimality Conditions for Vector Optimization

  • María C. Maciel
  • Sandra A. Santos
  • Graciela N. Sottosanto
Article

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.

Keywords

Nonlinear vector optimization Pareto points Weak Pareto points Constraint qualifications Optimality conditions 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • María C. Maciel
    • 1
  • Sandra A. Santos
    • 2
  • Graciela N. Sottosanto
    • 3
  1. 1.Department of MathematicsSouthern National UniversityBahía BlancaArgentina
  2. 2.Department of Applied MathematicsState University of CampinasCampinasBrazil
  3. 3.Department of MathematicsComahue National UniversityNeuquénArgentina

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