An Approach to Optimality Conditions in Vector and Scalar Optimization

  • Alberto Cambini
  • Laura Martein


The implication of concavity in economics have suggested in the scalar case several kinds of generalization starting from the pioneering work of Arrow-Enthoven (1961).

The aim of this paper is to point out the role played by generalized concavity and by the tangent cone to the feasible region at a point, in stating several necessary and/or sufficient optimality conditions for a vector and scalar optimization problem.

Furthermore, in deriving F.John optimality conditions, the role of separations theorems is analyzed in order to suggest suitable formulations of Kuhn-Tucker conditions and a way for studying regularity conditions.


Scalar Case Tangent Cone Vector Optimization Problem Closed Convex Cone Separation Theorem 
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Copyright information

© Springer-Verlag Berlin · Heidelberg 1993

Authors and Affiliations

  • Alberto Cambini
  • Laura Martein
    • 1
  1. 1.Department of Statistics and Applied MathematicsUniversity of PisaItaly

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