On a Global Complexity Bound of the Levenberg‐Marquardt Method

On a Global Complexity Bound of the Levenberg‐Marquardt Method

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Article ID: iaor20108150
Volume: 147
Issue: 3
Start Page Number: 443
End Page Number: 453
Publication Date: Dec 2010
Journal: Journal of Optimization Theory and Applications
Authors: ,
Keywords: complexity
Abstract:

In this paper, we investigate a global complexity bound of the Levenberg‐Marquardt method (LMM) for the nonlinear least squares problem. The global complexity bound for an iterative method solving unconstrained minimization of φ is an upper bound to the number of iterations required to get an approximate solution, such that ‖∇φ(x)‖≤ϵ. We show that the global complexity bound of the LMM is O(ϵ -2).

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