On proper efficiencies in locally convex spaces -- a survey
type: Item
instance of: scholarly article
title: On proper efficiencies in locally convex spaces -- a survey
zbMATH Open document ID: 1027.90084
author: Jing Liu
author: Wen Song
published in: Acta Mathematica Vietnamica
publication date: 2002-09-11T00:00:00Z
review text: In the vector optimization theory it is important to identify the efficient points. There are many definitions of such points. Let \(X\) be a locally convex topological vector space, \(A\subset X\) is a nonempty subset of \(X\) and \(S\subset X\) is a closed convex pointed cone. In the paper there are given several definitions of efficient points respect to \(S\): efficient points, positive proper efficient points, Hurwicz proper efficient points, Henig proper efficient points, globally Henig efficient points, Benson proper efficient points, Global Borwein efficient points, superefficient points, Strict efficient points, Borwein proper efficient points, locally Henig proper efficient points, properly efficient points. The aim of the paper is to examine the relationship among these definitions. The figure with the relationships is given at the end of the paper.
Mathematics Subject Classification ID: 90C29
zbMATH DE Number: 1799505
zbMATH Keywords: vector optimization
zbMATH Keywords: efficient points
zbMATH Keywords: locally convex topological vector space
reviewed by: Tadeusz Trzaskalik
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1799505