Vector optimization problems via improvement sets
The authors introduce the concept of improvement sets and optimal points with respect to the preference relation given by an improvement set (a nonempty set \(E\) in \(\mathbb R^n\) is called an improvement set if it does not contain the origin and has a free disposal property: \(E+\mathbb R^n_+ \subseteq E\); and a point \(a\) of a nonempty set \(A\) in \(\mathbb R^n\) is \(E\)-optimal if \((a+E)\cap A=\emptyset\)). Then they establish some proreties of \(E\)-optimal points and an existence condition by means of separators (linear functions that are strictly positive on \(E\)).
scientific article; zbMATH DE number 5980385
scientific article