Regularity of Newton’s iteration for general parametric variational system
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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.
KeywordsNewton’s method parametric variational system (partial) metric regularity (partial) Lipschitz-like property
Mathematics Subject Classification49J53 49M37 65J15 90C31
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).