Scalarization in vector optimization with arbitrary domination sets. (2nd August 2020) - Weidner, Petra
Abstract : In this paper, vector optimization problems with arbitrary domination sets are studied. Scalarization results for efficient and weakly efficient elements of these problems are proved, where especially Gerstewitz functionals and order unit norms are used. A surrogate for the weakly efficient point set is investigated, which is of special interest for domination sets with an empty algebraic interior. The study includes the consideration of perturbed problems. In general, we admit any linear space as image space of the vector optimization problem and do not assume convexity of the feasible point set or of the domination set. Nevertheless, several statements refer to the case that the domination set is an ordering cone. The results can be applied to determine optimal elements which are defined by relations, especially in decision making. Furthermore, they constitute a base for the systematic investigation of many scalarizing problems in multiobjective optimization. This is illustrated for the Hurwicz Rule in decision making under uncertainty.