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On the vectorial Ekeland’s variational principle and minimal points in product spaces. (English) Zbl 0997.49019
Taking into account that the scalar Ekeland’s variational principle is equivalent to the existence of a minimal point of the epigraph of the corresponding function with respect to an appropriate order, or to the existence of maximal points with respect to cones, satisfying some additional conditions, the authors obtain several minimal point theorems in product spaces and the corresponding variants of the vectorial Ekeland’s variational principle.

MSC:
49J53Set-valued and variational analysis
90C29Multi-objective programming; goal programming