Some Iterative Methods for Solving Nonconvex Bifunction Equilibrium Variational Inequalities

Some Iterative Methods for Solving Nonconvex Bifunction Equilibrium Variational Inequalities

We introduce and consider a new class of equilibrium problems and variational inequalities involving bifunction, which is called the nonconvex bifunction equilibrium variational inequality. We suggest and analyze some iterative methods for solving the nonconvex bifunction equilibrium variational inequalities using the auxiliary principle technique. We prove that the convergence of implicit meth...

Iterative Methods for Solving Nonconvex Equilibrium Variational Inequalities

n this paper, we introduce and consider a new class of equilibrium problems and variational inequalities which is called the nonconvex equilibrium variational inequality. We suggest and analyze some iterative methods for solving the nonconvex equilibrium variational inequalities using the auxiliary principle technique. We prove that the convergence of implicit method requires only monotonicity....

On nonconvex bifunction variational inequalities

In this paper, we introduce and consider a new class of variational inequalities, which is called the nonconvex bifunction variational inequality. We suggest and analyze some iterative methods for solving nonconvex bifunction variational inequalities using the auxiliary principle technique.We prove that the convergence of implicit method requires only pseudomonotonicity, which is weaker conditi...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

Some iterative methods for general nonconvex variational inequalities

In this paper, we suggest and analyze some three-step iterativemethods for solving general nonconvex variational inequalities using the technique of updating the solution. We show that the convergence of these iterativemethods requires only the partially relaxed strongly monotonicity which is a weaker condition than cocoerciveness.We are also discuss several special cases. Our method of proof i...