On proper efficiencies in locally convex spaces -- a survey
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.
scientific article; zbMATH DE number 1799505