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



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.


Set-valued mappings Lipschitz-like mappings Generalized equations Gauss–Newton-type method Semi-local convergence 



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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© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of MathematicsZhejiang UniversityHangzhouP.R. China
  2. 2.Department of MathematicsUniversity of RajshahiRajshahiBangladesh
  3. 3.Department of MathematicsZhejiang Normal UniversityJinhuaP.R. China
  4. 4.Department of MathematicsNational Cheng Kung UniversityTainanTaiwan

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