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Zbl 1152.49016
Araya, Yousuke
Ekeland's variational principle and its equivalent theorems in vector optimization. (English)
[J] J. Math. Anal. Appl. 346, No. 1, 9-16 (2008). ISSN 0022-247X

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 2000:
*49J53 Set-valued and variational analysis
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
49J27 Optimal control problems in abstract spaces (existence)

Keywords: Ekeland's variational principle; Caristi's fixed point theorem; Takahashi's nonconvex minimization theorem; vector-valued function; nonlinear scalarization

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