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A modified Newton-secant method for solving nonsmooth generalized equations

    Vitaliano de Sousa Amaral Affiliation
    ; Paulo Sérgio Marques dos Santos Affiliation
    ; Gilson N. Silva Affiliation
    ; Sissy Souza Affiliation

Abstract

In this paper, we study the solvability of nonsmooth generalized equations in Banach spaces using a modified Newton-secant method, by assuming a Hölder condition. Also, we generalize a Dennis-Moré theorem to characterize the superlinear convergence of the proposed method applied to nonsmooth generalized equations under strong metric subregularity. Numerical examples are provided to illustrate the effectiveness of our approach.

Keyword : Newton-Kantorovich theorem, divided differences, Newton-secant method, generalized equations

How to Cite
de Sousa Amaral, V., dos Santos, P. S. M., Silva, G. N., & Souza, S. (2024). A modified Newton-secant method for solving nonsmooth generalized equations. Mathematical Modelling and Analysis, 29(2), 347–366. https://doi.org/10.3846/mma.2024.18680
Published in Issue
Mar 26, 2024
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