On the solution of generalized equations and variational inequalities

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 Fréchet-differentiable function, and g is a maxi...

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Autores principales:	Argyros,Ioannis K, Hilout,Saïd
Lenguaje:	English
Publicado:	Universidad de La Frontera. Departamento de Matemática y Estadística. 2011
Materias:	Generalized equation variational inequality nonlinear complementarity problem nonlinear operator equation Kantorovich theorem generalized Newton’s method center-Lipschitz condition
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462011000100004
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spelling	oai:scielo:S0719-064620110001000042018-10-08On the solution of generalized equations and variational inequalitiesArgyros,Ioannis KHilout,Saïd Generalized equation variational inequality nonlinear complementarity problem nonlinear operator equation Kantorovich theorem generalized Newton’s method center-Lipschitz condition 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 Fréchet-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.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.13 n.1 20112011-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462011000100004en10.4067/S0719-06462011000100004
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Generalized equation variational inequality nonlinear complementarity problem nonlinear operator equation Kantorovich theorem generalized Newton’s method center-Lipschitz condition
spellingShingle	Generalized equation variational inequality nonlinear complementarity problem nonlinear operator equation Kantorovich theorem generalized Newton’s method center-Lipschitz condition Argyros,Ioannis K Hilout,Saïd On the solution of generalized equations and variational inequalities
description	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 Fréchet-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.
author	Argyros,Ioannis K Hilout,Saïd
author_facet	Argyros,Ioannis K Hilout,Saïd
author_sort	Argyros,Ioannis K
title	On the solution of generalized equations and variational inequalities
title_short	On the solution of generalized equations and variational inequalities
title_full	On the solution of generalized equations and variational inequalities
title_fullStr	On the solution of generalized equations and variational inequalities
title_full_unstemmed	On the solution of generalized equations and variational inequalities
title_sort	on the solution of generalized equations and variational inequalities
publisher	Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate	2011
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462011000100004
work_keys_str_mv	AT argyrosioannisk onthesolutionofgeneralizedequationsandvariationalinequalities AT hiloutsaid onthesolutionofgeneralizedequationsandvariationalinequalities
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On the solution of generalized equations and variational inequalities

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