On convergence and convergence rates for Ivanov and Morozov regularization and application to some parameter identification problems in elliptic PDEs. (4th April 2018)

• Record Type: Journal Article
• Authors: Kaltenbacher, Barbara; Klassen, Andrej
• Is Part Of: Inverse problems. Volume 34:Number 5(2018:May)
• Publication Date: 2018-04-04
• Subjects: quasi solutions -- method of residuals -- nonlinear inverse problems -- parameter identification; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aab739
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this paper we provide a convergence analysis of some variational methods alternative to the classical Tikhonov regularization, namely Ivanov regularization (also called the method of quasi solutions) with some versions of the discrepancy principle for choosing the regularization parameter, and Morozov regularization (also called the method of the residuals). After motivating nonequivalence with Tikhonov regularization by means of an example, we prove well-definedness of the Ivanov and the Morozov method, convergence in the sense of regularization, as well as convergence rates under variational source conditions. Finally, we apply these results to some linear and nonlinear parameter identification problems in elliptic boundary value problems.