Local convergence of exact and inexact newton’s methods for subanalytic variational inclusions

• Cabuzel, Catherine ^[1] ; Pietrus, Alain ^[1] ; Burnet, Steeve ^[1]
  1. [1] Laboratoire LAMIA-EA 4540, Université des Antilles et de la Guyane, Département de Mathématiques et Informatique, Campus de Fouillole, F–97159 Pointe–à–Pitre, France.
• Localización: Revista de Matemática: Teoría y Aplicaciones, ISSN 2215-3373, ISSN-e 2215-3373, Vol. 22, Nº. 1, 2015, págs. 31-47
• Idioma: inglés
• DOI: 10.15517/rmta.v22i1.17519
• Enlaces
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• Resumen

  • This paper deals with the study of an iterative method for solving a variational inclusion of the form 0 ∈ f (x)+F (x) where f is a locally Lipschitz subanalytic function and F is a set-valued map from Rn to the closed subsets of Rn. To this inclusion, we firstly associate a Newton then secondly an Inexact Newton type sequence and with some semistability and hemistability properties of the solution x∗ of the previous inclusion, we prove the existence of a sequence which is locally superlinearly convergent.

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