A new variant of Ekeland's variational principle for set-valued maps

In this article, following the idea used by Gopfert et al. [A. Gopfert, Chr. Tammer and C. Zalinescu (2000). On the vectorial Ekeland's variational principle and minimal points in-product spaces. Nonlinear Analysis, Theory, Methods & Applications, 39, 909-922] to derive an Ekeland's variational principle for vector-valued functions, we derive a new variant of Ekeland's variational principle for set-valued maps. Finally, we apply this variational principle to obtain an approximate necessary optimality condition for a class of set-valued optimization problems.