Startseite A projected homotopy perturbation method for nonlinear inverse problems in Banach spaces
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A projected homotopy perturbation method for nonlinear inverse problems in Banach spaces

  • Yuxin Xia ORCID logo , Bo Han EMAIL logo und Wei Wang
Veröffentlicht/Copyright: 31. März 2023

Abstract

In this paper, we propose and analyze a projected homotopy perturbation method based on sequential Bregman projections for nonlinear inverse problems in Banach spaces. To expedite convergence, the approach uses two search directions given by homotopy perturbation iteration, and the new iteration is calculated as the projection of the current iteration onto the intersection of stripes decided by above directions. The method allows to use L 1 -like penalty terms, which is significant to reconstruct sparsity solutions. Under reasonable conditions, we establish the convergence and regularization properties of the method. Finally, two parameter identification problems are presented to indicate the effectiveness of capturing the property of the sparsity solutions and the acceleration effect of the proposed method.

MSC 2020: 65J20; 65J22; 47H12

Award Identifier / Grant number: 12271129

Award Identifier / Grant number: 12071184

Funding statement: The work of Y. Xia and B. Han are supported by the National Natural Science Foundation of China (No. 12271129). The work of W. Wang is supported by the National Natural Science Foundation of China (No. 12071184) and the Top-level Talent Project of Zhejiang Province.

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Received: 2021-01-28
Revised: 2022-10-28
Accepted: 2022-10-30
Published Online: 2023-03-31
Published in Print: 2023-12-01

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