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A class of homotopy with regularization for nonlinear ill-posed problems in Hilbert space

  • Minghui Liu EMAIL logo and Fuming Ma
Published/Copyright: December 18, 2018

Abstract

Nonlinear ill-posed problems arise in many inverse problems in Hilbert space. We investigate the homotopy method, which can obtain global convergence to solve the problems. The “homotopy with Tikhonov regularization” and “homotopy without derivative” are developed in this paper. The existence of the homotopy curve is proved. Several numerical schemes for tracing the homotopy curve are given, including adaptive tracing skills. Compared to the regularized Newton method, the numerical examples show that our proposed methods are stable and effective.

MSC 2010: 65N20; 65H20

Award Identifier / Grant number: 11626230

Award Identifier / Grant number: 11771180

Funding statement: The first author was supported by the National Natural Science Foundation of China (NSFC) Grant 11626230, and the second author was supported by the National Natural Science Foundation of China (NSFC) Grant 11771180.

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Received: 2017-11-21
Revised: 2018-10-07
Accepted: 2018-11-19
Published Online: 2018-12-18
Published in Print: 2019-08-01

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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