Extended Newton-type Method for Nonsmooth Generalized Equation under n,α-point-based Approximation

M. Z. Khaton, M. H. Rashid and Attila Gil Nyi

International Journal of Mathematics and Mathematical Sciences, 2022, vol. 2022, 1-17

Abstract: Let X and Y be Banach spaces and Ω⊆X. Let f:Ω⟶Y be a single valued function which is nonsmooth. Suppose that F:X⇉2Y is a set-valued mapping which has closed graph. In the present paper, we study the extended Newton-type method for solving the nonsmooth generalized equation 0∈fx+Fx and analyze its semilocal and local convergence under the conditions that f+F−1 is Lipschitz-like and f admits a certain type of approximation which generalizes the concept of point-based approximation so-called n,α-point-based approximation. Applications of n,α-point-based approximation are provided for smooth functions in the cases n=1 and n=2 as well as for normal maps. In particular, when 0

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:7108996

DOI: 10.1155/2022/7108996

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