arXiv subjects
Publications and source records attributed to Elena-Andreea Florea.
We address a problem posed in [1] by demonstrating through an example that, in the absence of separability, the property of sequential cone compactness does not generally imply cone compactness.
We explore the possibility to derive basic calculus rules for some subdifferential constructions associated to set-valued maps between normed vector spaces. Then, we use these results in order to write optimality conditions for a special kind of solutions for set optimization problems.
We discuss, on finite and infinite dimensional normed vector spaces, some versions of Radström cancellation law (or lemma) that are suited for applications to set optimization problems. In this sense, we call our results "conic" variants of the celebrated result of Radström, since they involve the presence of an ordering cone on the underlying space. Several adaptations to this context of some topological properties of sets are studied and some applications to subdifferential calculus associated to set-valued maps and to necessary optimality conditions for constrained set optimization problems are given. Finally, a stability problem is considered.
We introduce and study a notion of directional Pareto minimality with respect to a set that generalizes the classical concept of Pareto efficiency. Then we give separate necessary and sufficient conditions for the newly introduced efficiency and several situations concerning the objective mapping and the constraints are considered. In order to investigate different cases, we adapt some well-known constructions of generalized differentiation and the connections with some recent directional regularities come naturally into play. As a consequence, several techniques from the study of genuine Pareto minima are considered in our specific situation.