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A generalization of Ekeland’s variational principle. (English) Zbl 0817.90098
Summary: Ekeland’s variational principle is a very deep assertion about the existence of an optimal solution of a slightly perturbed optimization problem in a neighborhood of an \(\varepsilon\)-optimal solution of the original problem. It plays an important role for developing necessary optimality conditions and other theoretical results. In this paper we give an extension of Ekeland’s theorem for vector optimization problems in general spaces where we use a concept of \(\varepsilon\)-efficiency which can be considered as a generalization of the concept of Loridan introduced for the finite-dimensional case. Our results differ essentially from other known generalizations of Ekeland’s theorem given by Loridan, Nemeth and Khanh in the assumptions, in the assertion and in the proof.

MSC:
90C29 Multi-objective and goal programming
90C26 Nonconvex programming, global optimization
65K10 Numerical optimization and variational techniques
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