Two-Variable Domination Structures and Applications in Vector Optimization

Abstract

In this paper, we introduce and study domination structures in real topological Hausdorff linear spaces that take into account the two involved points at each comparison. These binary relations are then applied to define notions of minimizer of a set and optimality concepts for vector optimization problems in the usual way, and their basic properties are obtained. Results on nonlinear scalarization to characterize them are also stated, which can be applied to vector optimization problems with variable ordering structures where the known ones do not work. Comparisons with results of the literature and illustrative examples are given as well.