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Convergence Rate of The Trust Region Method for Nonlinear Equations Under Local Error Bound Condition

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An Erratum to this article was published on 14 August 2006

Abstract

In this paper, we present the new trust region method for nonlinear equations with the trust region converging to zero. The new method preserves the global convergence of the traditional trust region methods in which the trust region radius will be larger than a positive constant. We study the convergence rate of the new method under the local error bound condition which is weaker than the nonsingularity. An example given by Y.X. Yuan shows that the convergence rate can not be quadratic. Finally, some numerical results are given.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, P.R. China

    Jinyan Fan

  2. Division of Computational Science, E-Institute of Shanghai Universities,SJTU, P.R. China

    Jinyan Fan

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  1. Jinyan Fan
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Additional information

This work is supported by Chinese NSFC grants 10401023 and 10371076, Research Grants for Young Teachers of Shanghai Jiao Tong University, and E-Institute of Computational Sciences of Shanghai Universities.

An erratum to this article is available at http://dx.doi.org/10.1007/s10589-006-9594-3.

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Fan, J. Convergence Rate of The Trust Region Method for Nonlinear Equations Under Local Error Bound Condition. Comput Optim Applic 34, 215–227 (2006). https://doi.org/10.1007/s10589-005-3078-8

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  • DOI: https://doi.org/10.1007/s10589-005-3078-8

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