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Convergence and Iteration Complexity Analysis of a Levenberg-Marquardt Algorithm for Zero and Non-zero Residual Inverse Problems

Y. Diouane (youssef.diouane***at***isae.fr)
E. Bergou (elhoucine.bergou***at***inra.fr)
V. Kungurtsev (vyacheslav.kungurtsev***at***fel.cvut.cz)

Abstract: The Levenberg-Marquardt algorithm is one of the most popular algorithms for the solution of nonlinear least squares problems. In this paper, we propose and analyze the global and local convergence results of a novel Levenberg-Marquardt method for solving general nonlinear least squares problems. The proposed algorithm enjoys strong convergence properties (global convergence as well as local convergence) for least squares problems which do not necessarily have a zero residual solution, all without any additional globalization strategy. Furthermore, we proved worst-case iteration complexity bounds for the proposed algorithm. Preliminary numerical experiments confirm the theoretical behavior of our proposed algorithm.

Keywords: Nonlinear least squares problem, inverse problems, Levenberg-Marquardt method, global and local convergence, worst-case complexity bound, quadratic and linear convergence.

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Unconstrained Optimization )

Citation:

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Entry Submitted: 05/11/2017
Entry Accepted: 05/11/2017
Entry Last Modified: 01/30/2018

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