A Hybrid Inertial Projection-proximal Method for Variational Inequalities

An inexact alternating direction method with SQP regularization for the structured variational inequalities

In this paper, we propose an inexact alternating direction method with square quadratic proximal  (SQP) regularization for  the structured variational inequalities. The predictor is obtained via solving SQP system  approximately  under significantly  relaxed accuracy criterion  and the new iterate is computed directly by an explicit formula derived from the original SQP method. Under appropriat...

Hybrid Proximal-Point Methods for Systems of Generalized Equilibrium Problems and Maximal Monotone Operators in Banach Spaces

In this paper, by using Bregman’s technique, we introduce and study the hybrid proximal-point methods for finding a common element of the set of solutions to a system of generalized equilibrium Problems and zeros of a finite family of maximal monotone operators in reflexive Banach spaces. Strong convergence results of the proposed hybrid proximal-point algorithms are also established under some...

Variational inequalities on Hilbert $C^*$-modules

We introduce variational inequality problems on Hilbert $C^*$-modules and we prove several existence results for variational inequalities defined on closed convex sets. Then relation between variational inequalities, $C^*$-valued metric projection and fixed point theory  on  Hilbert $C^*$-modules is studied.

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

Convergence rate analysis of iteractive algorithms for solving variational inequality problems

We present a unified convergence rate analysis of iterative methods for solving the variational inequality problem. Our results are based on certain error bounds; they subsume and extend the linear and sublinear rates of convergence established in several previous studies. We also derive a new error bound for γ -strictly monotone variational inequalities. The class of algorithms covered by our ...