Set-Valued Analysis

, Volume 2, Issue 1–2, pp 207–218 | Cite as

Convergence of the efficient sets

  • Dinh The Luc
  • R. Lucchetti
  • C. Maliverti
Article

Abstract

LetAn,n=1, 2, ... be nonempty subsets of a linear metric spaceE andCn, n=1, 2, ... convex cones ofE. We consider the efficient sets Min(An, Cn) and the aim of this paper is to show that under suitable conditions, the convergence ofAn andCn toA andC respectively, implies the convergence of Min(An,Cn) to Min(A, C). Several illustrative examples are given which clarify the results.

Mathematics Subject Classifications (1991)

49A50 48B50 

Key words

Efficient points Pareto stability Kuratowski-Painlevé and Attouch-Wets convergences 

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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Dinh The Luc
    • 1
  • R. Lucchetti
    • 2
  • C. Maliverti
    • 3
  1. 1.Institute of MathematicsHanoïVietnam
  2. 2.Dipartimento di MatematicaUniversità di MilanoMilanoItaly
  3. 3.Département de MathématiquesLimogesFrance

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