Journal of Optimization Theory and Applications

, Volume 29, Issue 4, pp 573–614 | Cite as

The structure of admissible points with respect to cone dominance

  • G. R. Bitran
  • T. L. Magnanti
Contributed Papers

Abstract

We study the set of admissible (Pareto-optimal) points of a closed, convex setX when preferences are described by a convex, but not necessarily closed, cone. Assuming that the preference cone is strictly supported and making mild assumptions about the recession directions ofX, we extend a representation theorem of Arrow, Barankin, and Blackwell by showing that all admissible points are either limit points of certainstrictly admissible alternatives or translations of such limit points by rays in the closure of the preference cone. We also show that the set of strictly admissible points is connected, as is the full set of admissible points.

Relaxing the convexity assumption imposed uponX, we also consider local properties of admissible points in terms of Kuhn-Tucker type characterizations. We specify necessary and sufficient conditions for an element ofX to be a Kuhn-Tucker point, conditions which, in addition, provide local characterizations of strictly admissible points.

Key Words

Vector optimization multiple objective optimization cone dominance efficient points Pareto optimality optimality conditions 

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Copyright information

© Plenum Publishing Corporation 1979

Authors and Affiliations

  • G. R. Bitran
    • 1
  • T. L. Magnanti
    • 1
  1. 1.Sloan School of ManagementMassachusetts Institute of TechnologyCambridge

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