In this paper, we consider a system of generalized variational inequalities. We introduce an iterative algorithm for the system of generalized variational inequalities and study the algorithmic convergence analysis. Strong convergence theorems are established. The results presented in this paper mainly improve and extend the corresponding results announced by many others. AMS subject classifica...

This paper proposes an additive Schwarz method for variational inequalities and their approximations by finite element methods. The Schwarz domain decomposition method is proved to converge with a geometric rate depending on the decomposition of the domain. The result is based on an abstract framework of convergence analysis established for general variational inequalities in Hilbert spaces.

In this paper, we introduce some gap functions for set-valued mixed variational inequalities under suitable conditions. We further use these gap functions to study global error bounds for the solutions of set-valued mixed variational inequalities in Hilbert spaces. The results presented in this paper generalize and improve some corresponding known results in literatures.

In this paper, a class of generalized invex functions, called [Formula: see text]-invex functions, is introduced, and some examples are presented to illustrate their existence. Then we consider the relationships of solutions between two types of vector variational-like inequalities and multi-objective programming problem. Finally, the existence results for the discussed variational-like inequal...

Variational inequalities over sets defined by systems of equalities and inequalities are considered. A new reformulation of the KKT-conditions of the variational inequality as a system of equations is proposed. A related unconstrained minimization reformulation is also investigated. As a by-product of the analysis, a new characterization of strong regularity of KKT-points is given.

We consider a general coercivity condition for multi-valued variational inequalities and show that this condition ensures both convergence of the Tikhonov-Browder regularization method and existence of solutions to the initial and perturbed problems. Applications of this approach to partitionable multi-valued variational inequalities utilizing extensions of order monotonicity properties are als...

Recently, variational inequality theory has been extended and applied in various directions, see [6, 7, 8, 9, 10] and the references therein. In particular, Ding [1, 2, 3], and Ding and Tan [4] studied the existence of solutions for several nonlinear variational-like inequalities in reflexive Banach spaces. In this paper, a new class of general nonlinear variational-like inequalities in reflexi...