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

Published: 2012/10/03

Global Optimization, Global Optimization Theory, Multi-Criteria Optimization abb theorem, augmented dual cone, bishop--phelps cone, proper efficiency, separation theorem, sublinear support functionals, vector optimization Short URL: https://optimization-online.org/?p=12180

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.

Citation

Department of Industrial Engineering, Anadolu University, Eskisehir, TUrkey

Article

Download

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