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Newton’s Method for Convex Optimization

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Advances in Iterative Methods for Nonlinear Equations

Part of the book series: SEMA SIMAI Springer Series ((SEMA SIMAI,volume 10))

Abstract

In this chapter we deal with the convex optimization problem (COP). Using the generalized-Newton’s algorithm (GNA) we generate a sequence that converges to a solution of the COP. We use weak-center and weak Lipschitz-type conditions in our semilocal convergence analysis leading to a finer convergence analysis than in earlier studies. Numerical examples where earlier sufficient convergence conditions are not satisfied but our conditions are satisfied are also presented in this chapter.

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Acknowledgements

This scientific work has been supported by the ‘Proyecto Prometeo’ of the Ministry of Higher Education Science, Technology and Innovation of the Republic of Ecuador.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Cameron University, Lawton, OK, 73505, USA

    Ioannis K. Argyros

  2. Departamento de Matemática, Escuela Politécnica Nacional, Quito, Ecuador

    Daniel González

Authors
  1. Ioannis K. Argyros
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  2. Daniel González
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Correspondence to Ioannis K. Argyros .

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Editors and Affiliations

  1. Departamento de Matemática, Aplicada y Estadística Universidad Politécnica de Cartagena, Cartagena, Spain

    Sergio Amat

  2. Departamento de Matemática, Aplicada y Estadística Universidad Politécnica de Cartagena, Cartagena, Spain

    Sonia Busquier

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Argyros, I.K., González, D. (2016). Newton’s Method for Convex Optimization. In: Amat, S., Busquier, S. (eds) Advances in Iterative Methods for Nonlinear Equations. SEMA SIMAI Springer Series, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-319-39228-8_3

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