Generalized Systems of Variational Inequalities and Projection Methods for Inverse-Strongly Monotone Mappings

Generalized Systems of Variational Inequalities and Projection Methods for Inverse-Strongly Monotone Mappings

We introduce an iterative sequence for finding a common element of the set of fixed points of a nonexpansive mapping and the solutions of the variational inequality problem for three inversestrongly monotone mappings. Under suitable conditions, some strong convergence theorems for approximating a common element of the above two sets are obtained. Moreover, using the above theorem, we also apply...

Generalized Variational Inequalities Involving Relaxed Monotone Mappings and Nonexpansive Mappings

A Relaxed Extra Gradient Approximation Method of Two Inverse-Strongly Monotone Mappings for a General System of Variational Inequalities, Fixed Point and Equilibrium Problems

Generalized Projection Method for Non-lipschitz Multivalued Monotone Variational Inequalities

We generalize the projection method for solving strongly monotone multivalued variational inequalities when the cost operator is not necessarily Lipschitz. At each iteration at most one projection onto the constrained set is needed. When the convex constrained set is not polyhedral, we embed the proposed method in a polyhedral outer approximation procedure. This allows us to obtain the projecti...

Interior projection-like methods for monotone variational inequalities

We propose new interior projection type methods for solving monotone variational inequalities. The methods can be viewed as a natural extension of the extragradient and hyperplane projection algorithms, and are based on using non Euclidean projection-like maps. We prove global convergence results and establish rate of convergence estimates. The projection-like maps are given by analytical formu...