%0 Journal Article %T Regularization Methods to Approximate Solutions of Variational Inequalities %A Nguyen Van Kinh %J Open Journal of Optimization %P 34-60 %@ 2325-7091 %D 2023 %I Scientific Research Publishing %R 10.4236/ojop.2023.122004 %X In this paper, we study the regularization methods to approximate the solutions of the variational inequalities with monotone hemi-continuous operator having perturbed operators arbitrary. Detail, we shall study regularization methods to approximate solutions of following variational inequalities: $\"\"$ and $\"\"$ with operator A being monotone hemi-continuous form real Banach reflexive X into its dual space X*, but instead of knowing the exact data (y₀, A), we only know its approximate data $\"\"$ satisfying certain specified conditions and D is a nonempty convex closed subset of X; the real function f defined on X is assumed to be lower semi-continuous, convex and is not identical to infinity. At the same time, we will evaluate the convergence rate of the approximate solution. The regularization methods here are different from the previous ones. %K Ill-Posed Problem %K Variational Inequality %K Regularization Method %K Monotone Operator %K Hemi-Continuous Operator %K Lower Semi-Continuous Function %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=125505