ABSTRACT
In this chapter, the authors begin by providing necessary optimality conditions in terms of Bouligand derivatives for the constrained robust efficiency notion in the variable ordering structures setting. They aim to present some new developments for the theory of vector optimization with variable ordering structures under the paradigm introduced, that is in the natural setting when the objective and the ordering mappings share the same input and output space. This corresponds, intuitively, to the situation when the preferences of the decision maker may vary with respect to the same parameters as the objective itself. The authors introduce the notation and the main tools of nonlinear analysis. They deal with the efficiency concepts they study in the framework of vector optimization with the variable ordering structures for the case of the same input and output spaces, both for objective and ordering multifunctions.
