Six set scalarizations based on the oriented distance: properties and application to set optimization
Bienvenido Jiménez, Vicente Novo, A. Vílchez · Optimization · 2019
In the framework of normed spaces ordered by a convex cone not necessarily solid, we present six set scalarization functions which are extensions of the oriented distance of Hiriart-Urruty. We investigate their relationships and study some of their properties. Moreover, by means of these functions, we characterize the six set relations given by Kuroiwa. Finally, considering these set relations, we define six set optimization problems with the set criterion of solution and we derive several necessary and sufficient minimality conditions by using the six set scalarization functions above-mentioned. Illustrative examples are also given.