We suggest and analyze some implicit iterative methods for solving the extended general nonconvex variational inequalities using the projection technique. We show that the convergence of these iterative methods requires only the gh-pseudomonotonicity, which is a weaker condition than gh-monotonicity. We also discuss several special cases. Our method of proof is very simple as compared with othe...

In this paper, we use the auxiliary principle technique to suggest and analyze an implicit iterative method for solving bifunction variational inequalities. We also study the convergence criteria of this new method under pseudomonotonicity condition.

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...

We consider a new class of equilibrium problems, known as hemiequilibrium problems. Using the auxiliary principle technique, we suggest and analyze a class of iterative algorithms for solving hemiequilibrium problems, the convergence of which requires either pseudomonotonicity or partially relaxed strong monotonicity. As a special case, we obtain a new method for hemivariational inequalities. S...

We use the auxiliary principle technique to suggest and analyze a proximal point method for solving the mixed variational inequalities on the Hadamard manifold. It is shown that the convergence of this proximal point method needs only pseudomonotonicity, which is a weaker condition than monotonicity. Some special cases are also considered. Results can be viewed as refinement and improvement of ...

In this paper we study a variational inequality over a product of sets, governed by a multi-valued mapping, in pseudomonotonicity conditions. We are interested in the existence of the solution and, when the inequality depends on a parameter, also in the behavior of the solution at perturbations of the parameter. Mathematics subject classification (2000): 47J20, 58E35, 49N60.

This paper concerns developing two hybrid proximal point methods (PPMs) for finding a common solution of some optimization-related problems. First we construct an algorithm to solve simultaneously an equilibrium problem and a variational inequality problem, combing the extragradient method for variational inequalities with an approximate PPM for equilibrium problems. Next we develop another alg...