A Descent-projection Method for Solving Monotone Structured 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...

Strong Convergence of a Double Projection-type Method for Monotone Variational Inequalities in Hilbert Spaces

We introduce a projection-type algorithm for solving monotone variational inequality problems in real Hilbert spaces. We prove that the whole sequence of iterates converges strongly to a solution of the variational inequality. The method uses only two projections onto the feasible set in each iteration in contrast to other strongly convergent algorithms which either require plenty of projection...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

A descent alternating direction method for monotone variational inequalities with separable structure

To solve a special class of variational inequalities with separable structure, this paper proposes a descent alternating direction method based on a new residual function. The most prominent characteristic of the method is that it is easily performed, in which, only some orthogonal projections and function evaluations are involved at each iteration, so its computational load is very tiny. Under...

A Descent Method for Nonsmooth Variational Inequalities via Regularization

in this paper we propose a descent method for solving variational inequality problems where the underlying operator is nonsmooth, locally Lipschitz, and monotone over a closed, convex feasible set. The idea is to combine a descent method for variational inequality problems whose operators are nonsmooth, locally Lipschitz, and strongly monotone, with the Tikonov-Browder regularization technique....