Solving variational inclusions by a multipoint iteration method under center-Hölder continuity conditions

Volume 34 / 2007

Catherine Cabuzel, Alain Pietrus Applicationes Mathematicae 34 (2007), 493-503 MSC: 49J53, 47H04, 65K10. DOI: 10.4064/am34-4-8

Abstract

We prove the existence of a sequence $(x_k)$ satisfying $0 \in f(x_k) +\sum _{i=1}^M a_i \nabla f(x_k+\beta_i(x_{k+1}-x_k))(x_{k+1}-x_k)+F(x_{k+1})$, where $f$ is a function whose second order Fréchet derivative $\nabla^2 f$ satifies a center-Hölder condition and $F$ is a set-valued map from a Banach space $X$ to the subsets of a Banach space $Y$. We show that the convergence of this method is superquadratic.

Authors

  • Catherine CabuzelLaboratoire Analyse, Optimisation, Contrôle
    Département de Mathématiques et Informatique
    Université des Antilles et de la Guyane
    Campus de Fouillole
    F-97159 Pointe-à-Pitre, France
    e-mail
  • Alain PietrusLaboratoire Analyse, Optimisation, Contrôle
    Département de Mathématiques et Informatique
    Université des Antilles et de la Guyane
    Campus de Fouillole
    F-97159 Pointe-à-Pitre, France
    e-mail

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