Cost Bifunction Research Articles

Partial proximal point method for nonmonotone equilibrium problems

We consider a general equilibrium problem defined on a convex set, whose cost bifunction may be nonmonotone. We show that this problem can be solved by the inexact partial proximal point method. These results can be viewed as a generalization of the known convergence properties of the usual proximal point method.

Application of the Proximal Point Method to Nonmonotone Equilibrium Problems

We consider a general equilibrium problem defined on a convex set, whose cost bifunction may not be monotone. We show that this problem can be solved by the inexact proximal point method if there exists a solution to the dual problem. An application of this approach to nonlinearly constrained problems is also suggested.

Combined Relaxation Method for Monotone Equilibrium Problems

A scalar equilibrium problem which involves a monotone differentiable cost bifunction is considered. For such bifunction, a skew-symmetric type property with respect to the partial gradients is established. This property enables us to construct a new combined relaxation method and essentially simplify its line search procedure. An application to an inverse equilibrium problem is also presented.