On Solutions of Variational Inequality Problems via Iterative Methods

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...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

Positive Solutions of Singular Dirichlet Problems via Variational Methods

In this paper, we establish the existence results for second order singular Dirichlet problems via variational methods. Some recent results are extended and improved. Examples are also given to illustrate the new results.

Augmented Lagrangian methods for variational inequality problems

We introduce augmented Lagrangian methods for solving finite dimensional variational inequality problems whose feasible sets are defined by convex inequalities, generalizing the proximal augmented Lagrangian method for constrained optimization. At each iteration, primal variables are updated by solving an unconstrained variational inequality problem, and then dual variables are updated through ...

iterative methods for equilibrium problems, variational inequalities and fixed points