Hein, Torsten : Multi-parameter regularization - convergence and convergence rates results

Author(s):

Hein, Torsten

Title:

Multi-parameter regularization - convergence and convergence rates results

Electronic source:

application/postscript

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 17, 2007

Mathematics Subject Classification:

47J06			[ Nonlinear ill-posed problems ]
49N45			[ Inverse problems ]
65J20			[ Improperly posed problems; regularization ]
91B28			[ Finance, portfolios, investment ]

Abstract:

In this paper we present a multi-parameter regularization approach for solving nonlinear ill-posed problems when a 'vector' of data is given. Based on the the convergence analysis for nonlinear Tikhonov regularization we show stability and convergence of the method. Additionally we prove convergence rates results by using Bregman distances and suggest a numerical algorithm for solving the underlying minimization problem in an efficient way. The advantage of considering multi-parameter regularization approaches is illustrated by an example arising in mathematical finance.

Keywords:

Inverse problem, nonlinear ill-posed problem, multi-parameter regularization, Bregman distance, convergence rates, Lagrangian methods

Language:

English

Publication time:

12 / 2007