Monotone Iterations for Eliptic Variational Inequalities

On the Monotone Mappings in CAT(0) Spaces

In this paper, we first introduce a monotone mapping and its resolvent in general metric spaces.Then, we give two new iterative methods  by combining the resolvent method with Halpern's iterative method and viscosity approximation method for  finding a fixed point of monotone mappings and a solution of variational inequalities. We prove convergence theorems of the proposed iterations  in ...

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

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

Proximal Methods for Variational Inequalities with Set-Valued Monotone Operators

A general approach to analyse convergence and rate of convergence of the proximal-like methods for variational inequalities with set-valued maximal monotone operators is developed. It is oriented to methods coupling successive approximation of the variational inequality with the proximal point algorithm as well as to related methods using regularization on a subspace and weak regularization. Th...

Dual extrapolation and its applications to solving variational inequalities and related problems

In this paper we suggest new dual methods for solving variational inequalities with monotone operators. We show that with an appropriate step-size strategy, our method is optimal both for Lipschitz continuous operators (O(12 ) iterations), and for the operators with bounded variations (O( 1 22 ) iterations). Our technique can be applied for solving nonsmooth convex minimization problems with kn...