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Regularity of Newton’s iteration for general parametric variational system

  • Wei OuyangEmail author
  • Binbin Zhang
Article
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Abstract

In this work, we apply the contraction mapping principle for set-valued mappings to study the Lipschitz-like property of the solution mapping to general parametric variational system obtained via canonical perturbation of a generalized equation. Then, under the assumptions of partial metric regularity and partial Lipschitz-like property, we obtained quadratic convergence of the iterative sequence when started close enough to the solution and provided estimates for the convergence parameters. Upon reconsidering all associated infinite sequences of Newton’s iterates as the image of a mapping defined on a sequence space, we established efficient conditions ensuring such a mapping to possess partial Lipschitz-like properties and also provided estimates of the moduli.

Keywords

Newton’s method parametric variational system (partial) metric regularity (partial) Lipschitz-like property 

Mathematics Subject Classification

49J53 49M37 65J15 90C31 
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Notes

Acknowledgements

The authors would like to express their gratitude to Michel Théra for his helpful comments and suggestions. This work was supported by National Natural Science Foundation of China (11801500, 11771384), Yunnan Provincial Science and Technology Department Research Fund (2017FD070), Yunnan Provincial Department of Education Research Fund (2019J0040) and the Fund for Fostering Talents in Kunming University of Science and Technology (KKSY 201807022).

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of MathematicsYunnan Normal UniversityKunmingPeople’s Republic of China
  2. 2.School of ScienceKunming University of Science and TechnologyKunmingPeople’s Republic of China

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