Range-relaxed criteria for choosing the Lagrange multipliers in the Levenberg-Marquardt method
Abstract
In this article we propose a novel strategy for choosing the Lagrange multipliers in the Levenberg-Marquardt method for solving ill-posed problems modeled by nonlinear operators acting between Hilbert spaces. Convergence analysis results are established for the proposed method, including: monotonicity of iteration error, geometrical decay of the residual, convergence for exact data, stability and semi-convergence for noisy data. Numerical experiments are presented for an elliptic parameter identification two-dimensional EIT problem. The performance of our strategy is compared with standard implementations of the Levenberg-Marquardt method (using a priori choice of the multipliers).
- Publication:
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arXiv e-prints
- Pub Date:
- November 2020
- DOI:
- arXiv:
- arXiv:2011.05890
- Bibcode:
- 2020arXiv201105890L
- Keywords:
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- Mathematics - Numerical Analysis;
- 65J20;
- 47J06
- E-Print:
- 25 pages, 3 figures, IMA Journal of Numerical Analysis (to appear)