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A Generalization of a Theorem of Arrow, Barankin and Blackwell to a Nonconvex Case

Refail Kasimbeyli(rkasimbeyli***at***anadolu.edu.tr)
Musa Mammadov(m.mammadov***at***ballarat.edu.au)

Abstract: The paper presents a generalization of a known density theorem of Arrow, Barankin, and Blackwell for properly efficient points defined as support points of sets with respect to monotonically increasing sublinear functions. This result is shown to hold for nonconvex sets of a reflexive Banach space partially ordered by a Bishop--Phelps cone.

Keywords: vector optimization, ABB theorem, Bishop--Phelps cone, separation theorem, sublinear support functionals, augmented dual cone, proper efficiency

Category 1: Global Optimization

Category 2: Global Optimization (Theory )

Category 3: Other Topics (Multi-Criteria Optimization )

Citation: Department of Industrial Engineering, Anadolu University, Eskisehir, TUrkey

Download: [PDF]

Entry Submitted: 10/03/2012
Entry Accepted: 10/03/2012
Entry Last Modified: 10/03/2012

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