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Convergence Analysis of the Gauss–Newton-Type Method for Lipschitz-Like Mappings

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Abstract

We introduce in the present paper a Gauss–Newton-type method for solving generalized equations defined by sums of differentiable mappings and set-valued mappings in Banach spaces. Semi-local convergence and local convergence of the Gauss–Newton-type method are analyzed.

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Acknowledgements

The authors thank the referees and the associate editor for their valuable comments and constructive suggestions which improved the presentation of this manuscript. Research work of the first author is fully supported by Chinese Scholarship Council, and research work of the third author is partially supported by National Natural Science Foundation (grant 11171300) and Zhejiang Provincial Natural Science Foundation (grant Y6110006) of China.

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Author notes

  1. M. H. Rashid

    Present address: Department of Mathematics, University of Rajshahi, Rajshahi, 6205, Bangladesh

Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, P.R. China

    M. H. Rashid & C. Li

  2. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, P.R. China

    S. H. Yu

  3. Department of Mathematics, National Cheng Kung University, Tainan, Taiwan

    S. Y. Wu

Authors
  1. M. H. Rashid
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  2. S. H. Yu
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  3. C. Li
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  4. S. Y. Wu
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Corresponding author

Correspondence to C. Li.

Additional information

Communicated by Nguyen Don Yen.

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Rashid, M.H., Yu, S.H., Li, C. et al. Convergence Analysis of the Gauss–Newton-Type Method for Lipschitz-Like Mappings. J Optim Theory Appl 158, 216–233 (2013). https://doi.org/10.1007/s10957-012-0206-3

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  • DOI: https://doi.org/10.1007/s10957-012-0206-3

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