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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 27, Issue 4


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

Minghui Liu
  • Corresponding author
  • School of Criminal Investigation and Counter Terrorism, People’s Public Security University of China, Beijing, P. R. China
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/ Fuming Ma
Published Online: 2018-12-18 | DOI: https://doi.org/10.1515/jiip-2017-0108


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.

Keywords: Homotopy with regularization; nonlinear ill-posed problems; numerical method

MSC 2010: 65N20; 65H20


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About the article

Received: 2017-11-21

Revised: 2018-10-07

Accepted: 2018-11-19

Published Online: 2018-12-18

Published in Print: 2019-08-01

Funding Source: National Natural Science Foundation of China

Award identifier / Grant number: 11626230

Award identifier / Grant number: 11771180

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.

Citation Information: Journal of Inverse and Ill-posed Problems, Volume 27, Issue 4, Pages 487–499, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2017-0108.

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