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The convergence analysis of inexact Gauss–Newton methods for nonlinear problems

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Abstract

In this paper, inexact Gauss–Newton methods for nonlinear least squares problems are studied. Under the hypothesis that derivative satisfies some kinds of weak Lipschitz conditions, the local convergence properties of inexact Gauss–Newton and inexact Gauss–Newton like methods for nonlinear problems are established with the modified relative residual control. The obtained results can provide an estimate of convergence ball for inexact Gauss–Newton methods.

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  1. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

    Jinhai Chen

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  1. Jinhai Chen
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Chen, J. The convergence analysis of inexact Gauss–Newton methods for nonlinear problems. Comput Optim Appl 40, 97–118 (2008). https://doi.org/10.1007/s10589-007-9071-7

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  • DOI: https://doi.org/10.1007/s10589-007-9071-7

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