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An Approach to Optimality Conditions in Vector and Scalar Optimization

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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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© 1993 Springer-Verlag Berlin · Heidelberg

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Cambini, A., Martein, L. (1993). An Approach to Optimality Conditions in Vector and Scalar Optimization. In: Diewert, W.E., Spremann, K., Stehling, F. (eds) Mathematical Modelling in Economics. Springer, Berlin, Heidelberg.

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-78510-8

  • Online ISBN: 978-3-642-78508-5

  • eBook Packages: Springer Book Archive