TITLE:
Regularization Methods to Approximate Solutions of Variational Inequalities
AUTHORS:
Nguyen Van Kinh
KEYWORDS:
Ill-Posed Problem, Variational Inequality, Regularization Method, Monotone Operator, Hemi-Continuous Operator, Lower Semi-Continuous Function
JOURNAL NAME:
Open Journal of Optimization,
Vol.12 No.2,
June
9,
2023
ABSTRACT: 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:andwith 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.