On the solution of generalized equations and variational inequalities

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DOI:

https://doi.org/10.4067/S0719-06462011000100004

Abstract

Uko and Argyros provided in [18] a Kantorovich–type theorem on the existence and uniqueness of the solution of a generalized equation of the form f(u)+g(u) ∋ 0, where f is a Fr´echet–differentiable function, and g is a maximal monotone operator defined on a Hilbert space. The sufficient convergence conditions are weaker than the corresponding ones given in the literature for the Kantorovich theorem on a Hilbert space. However, the convergence was shown to be only linear.

In this study, we show under the same conditions, the quadratic instead of the linear convergenve of the generalized Newton iteration involved.

Keywords

Generalized equation , variational inequality , nonlinear complementarity problem , nonlinear operator equation , Kantorovich theorem , generalized Newton‘s method , center–Lipschitz condition
  • Ioannis K. Argyros Cameron University, Department of Mathematics Sciences, Universidad Nacional Autónoma de México, Lawton, OK 73505, USA.
  • Saïd Hilout Poitiers University, Laboratoire de Mathématiques et Applications, Bd. Pierre et Marie Curie, Téléport 2, B.P. 30179, 86962 Futuroscope Chasseneuil Cedex, France.
  • Pages: 45–60
  • Date Published: 2011-03-01
  • Vol. 13 No. 1 (2011): CUBO, A Mathematical Journal

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Published

2011-03-01

How to Cite

[1]
I. K. Argyros and S. Hilout, “On the solution of generalized equations and variational inequalities”, CUBO, vol. 13, no. 1, pp. 45–60, Mar. 2011.

Issue

Vol. 13 No. 1 (2011): CUBO, A Mathematical Journal

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Articles