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Extended Newton-type method for nonlinear functions with values in a cone

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Abstract

In this paper, we consider the problem of finding solutions of nonlinear inclusion problems in Banach space. Using convex optimization techniques introduced by Robinson (Numer Math 19:341–347, 1972), a convergence theorem for Kantorovich-like methods is given, which improves the results of Yamamoto (Jpn J Appl Math 3(2):295–313, 1986; Numer Math 51(5):545–557, 1987) and Robinson (Numer Math 19:341–347, 1972). The result is compared with previously known results. Numerical examples further justify the theoretical results.

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Acknowledgements

The authors would like to thank the two anonymous referees for their constructive comments which have helped to substantially improve the presentation of the paper.

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Authors and Affiliations

  1. Centro das Ciências Exatas e das Tecnologias, Universidade Federal do Oeste da Bahia, Barreiras, BA, CEP 47808-021, Brazil

    G. N. Silva

  2. Departamento de Matemática, Parnaíba, Universidade Federal do Piauí, Parnaíba, PI, Brazil

    P. S. M. Santos & S. S. Souza

Authors
  1. G. N. Silva
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  2. P. S. M. Santos
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  3. S. S. Souza
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Correspondence to G. N. Silva.

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Communicated by Hector Ramirez.

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Silva, G.N., Santos, P.S.M. & Souza, S.S. Extended Newton-type method for nonlinear functions with values in a cone. Comp. Appl. Math. 37, 5082–5097 (2018). https://doi.org/10.1007/s40314-018-0617-3

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  • DOI: https://doi.org/10.1007/s40314-018-0617-3

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