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Existence of vector equilibria via Ekeland’s variational principle. (English) Zbl 1172.65032

The authors use a nonlinear scalarizing function to the case of a vector-valued function leading to a variational principle for the vector equilibrium problem. Then the authors obtain a Caristi-Kirk type fixed point theorem and an existence result for the vector equilibrium problem. The paper generalizes the vectorial Caristi-Kirk fixed point theorem and the vectorial Takahashi’s nonconvex minimization theorem.

MSC:

65K10 Numerical optimization and variational techniques
58E17 Multiobjective variational problems, Pareto optimality, applications to economics, etc.
90C29 Multi-objective and goal programming
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