A generalized variational principle and its application to equilibrium problems
The authors prove an extended version of the Ekeland variational principle for nonlinear equilibrium problems (EPs) in complete metric spaces, which admits perturbation functions. The cost bi-function should satisfy a triangle type inequality. This allows them to obtain an existence result for EPs in Euclidean spaces without convexity assumptions and to derive localization bounds for approximate equilibrium points. Next, extensions of these results for EPs on Cartesian product sets are also presented.
scientific article; zbMATH DE number 6161544
scientific article