Regularity analyses and approximation of nonlocal variational equality and inequality problems

Best approximation and variational inequality problems involving a simulation function

Regularized Iterative Stochastic Approximation Methods for Variational Inequality Problems

We consider a Cartesian stochastic variational inequality problem with a monotone map. For this problem, we develop and analyze distributed iterative stochastic approximation algorithms. Such a problem arises, for example, as an equilibrium problem in monotone stochastic Nash games over continuous strategy sets. We introduce two classes of stochastic approximation methods, each of which require...

Regularity results for nonlocal equations by approximation

We obtain C regularity estimates for nonlocal elliptic equations that are not necessarily translation invariant using compactness and perturbative methods and our previous regularity results for the translation invariant case.

Some Modified Extragradient Approximation Methods for Variational Inequality Problems and Equilibrium Problems of Nonexpansive Mappings

In this paper, we introduce a modified extragradient approximation method for finding the common element of the set of fixed points of nonexpansive mapping, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality. We show that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions. Ou...

The Uniform Asymptotical Regularity of Families of Mappings and Solutions of Variational Inequality Problems

In this paper our aim is to introduce a new class of procedure, the Uniformly Asymptotically Regular-class of procedures (UAR-precedures), showing some examples of procedures as for finite family of mappings, as for infinite family of mappings. Then by a UAR-procedure we prove the convergence of an implicit iterative method and of an explicit iterative method to the unique solution of a variati...