A global optimization approach to Berge equilibrium based on a regularized function

This work deals with a Berge equilibrium problem (BEP). Based on the existence results of Berge equilibrium of Nessah et al. (Appl Math Lett 20(8):926–932. 2007), we consider BEP with concave objective functions. The existence of Berge equilibrium has been proven. BEP reduces to nonsmooth optimization problem. Then using a regularized function, we reduce a problem of finding Berge equilibrium to a nonconvex global optimization problem with a differentiable objective functions. The later allows to apply optimization methods and algorithms to solve the original problem.