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Van Kinh, N., Chuong, N.M. and Gorenflo, R. (1996) Regularization Method for Nonlinear Variational Inequalities. Proceedings of the First National Workshop “Optimization and Control”, Quinhon, May 27 - June 1, 1996, 53-64. (Preprint: Nr. A-89-28, Freie Universitat, Berlin).

has been cited by the following article:

• TITLE: On the Regularization Method for Solving Ill-Posed Problems with Unbounded Operators

  AUTHORS: Nguyen Van Kinh

  KEYWORDS: Ill-Posed Problem, Regularization Method, Unbounded Linear Operator

  JOURNAL NAME: Open Journal of Optimization, Vol.11 No.2, June 15, 2022

  ABSTRACT: Let be a linear, closed, and densely defined unbounded operator, where X and Y are Hilbert spaces. Assume that A is not boundedly invertible. Suppose the equation Au=f is solvable, and instead of knowing exactly f only know its approximation satisfies the condition: In this paper, we are interested a regularization method to solve the approximation solution of this equation. This approximation is a unique global minimizer of the functional , for any , defined as follows: . We also study the stability of this method when the regularization parameter is selected a priori and a posteriori. At the same time, we give an application of this method to the weak derivative operator equation in Hilbert space.