Scalarization of Set-Valued Optimization Problems in Normed Spaces

This work focuses on scalarization processes for nonconvex set-valued optimization problems whose solutions are defined by the so-called l-type less order relation, the final space is normed and the ordering cone is not necessarily solid. A scalarization mapping is introduced, which generalizes the well-known oriented distance, and its main properties are stated. In particular, by choosing a suitable norm it is shown that it coincides with the generalization of the so-called Tammer-Weidner nonlinear separation mapping to this kind of optimization problems. After that, two concepts of solution are characterized in terms of solutions of associated scalar optimization problems defined through the new scalarization mapping.