joint work with Marius Durea, Marian Pantiruc
We introduce a type of directional regularity for mappings, making use of a special kind of minimal time function. We devise a new directional Ekeland Variational Principle, which we use to obtain necessary and sufficient conditions for directional regularity, formulated in terms of generalized differentiation objects. Stability of the directional regularity with respect to compositions and sums is analyzed. Finally, we apply this study to vector and scalar optimization problems with single and set-valued maps objectives.
joint work with Marius Durea, Elena-Andreea Florea
We study a notion of directional Pareto minimality that generalizes the classical concept of Pareto efficiency. Then, considering several situations concerning the objective mapping and the constraints, we give necessary and sufficient conditions for the directional efficiency. We investigate different cases and we propose some adaptations of well-known constructions of generalized differentiation. In this way, the connections with some recent directional regularities come into play. As a consequence, several techniques from the study of genuine Pareto minima are considered in our setting.
joint work with Elena-Andreea Florea
We study sufficient conditions for directional metric regularity of an epigraphical mapping in terms of generalized differentiation objects. The main feature proposed by our approach is the possibility to avoid the demanding assumption on the closedness of the graph of such a mapping. To this aim, we prove a version of Ekeland Variational Principle adapted to the situation we consider. Then, we apply our directional openness result to derive optimality conditions for directional Pareto minimality.