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Ekeland’s variational principle and its equivalent theorems in vector optimization. (English) Zbl 1152.49016
Summary: We present a simple proof of vectorial Ekeland’s variational principle, vectorial Caristi’s fixed point theorem and vectorial Takahashi’s nonconvex minimization theorem. Equivalences between the three theorems are also given.

MSC:
49J53Set-valued and variational analysis
47H10Fixed point theorems for nonlinear operators on topological linear spaces
49J27Optimal control problems in abstract spaces (existence)
References:
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