A modified Newton-secant method for solving nonsmooth generalized equations

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 general...

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Published inMathematical modelling and analysis Vol. 29; no. 2; pp. 347 - 366
Main Authors de Sousa Amaral, Vitaliano, dos Santos, Paulo Sérgio Marques, Silva, Gilson N., Souza, Sissy
Format Journal Article
LanguageEnglish
Published Vilnius Vilnius Gediminas Technical University 26.03.2024
Subjects
Banach spaces
divided differences
generalized equations
Generalized estimating equations
Mathematical analysis
Mathematical programming
Newton-Kantorovich theorem
Newton-secant method
Tests, problems and exercises
Trigonometrical functions
Brazil
generalized equations
Newton-secant method
divided differences
Newton-Kantorovich theorem
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ISSN1392-6292
1648-3510
1648-3510
DOI10.3846/mma.2024.18680

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Summary: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.
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ISSN:1392-6292
1648-3510
1648-3510
DOI:10.3846/mma.2024.18680