Implicit Iterative Method for Hierarchical Variational Inequalities

Implicit Iterative Method for Hierarchical Variational Inequalities

1 Scientific Computing Key Laboratory of Shanghai Universities, Department of Mathematics, Shanghai Normal University, Shanghai 200234, China 2 Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India 3 Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia 4 Department of Applied Mathematics, National Sun Yat-se...

A new iterative method for variational inequalities

It is well known that the variational inequalities are equivalent to the fixed point problems. Using this equivalence, we suggest and consider a new three-step iterative method for solving variational inequalities. The new iterative method is obtained by using three steps under suitable conditions. We prove that the new method is globally convergent. Our results can be viewed as significant ext...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

New Implicit Method for General Nonconvex Variational Inequalities

In this paper, we suggest and analyze a new implicit iterative projection method for solving general nonconvex variational inequalities. We prove that the new implicit method is equivalent to the modified projection method. Using this alternative equivalence between the implicit method and the modified projection, we prove that the convergence of the new implicit method requires only the partia...

A modified inexact implicit method for mixed variational inequalities

MSC: 65K10 90C25 90C30 Keywords: Mixed variational inequalities Implicit methods Resolvent operator Inexact methods Self-adaptive rules a b s t r a c t In this paper, we suggest and analyze an inexact implicit method with a variable parameter for mixed variational inequalities by using a new inexactness restriction. Under certain conditions, the global convergence of the proposed method is prov...