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

Catherine Cabuzel¹ ; Alain Pietrus¹

¹ Laboratoire Analyse, Optimisation, Contrôle Département de Mathématiques et Informatique Université des Antilles et de la Guyane Campus de Fouillole F-97159 Pointe-à-Pitre, France

Applicationes Mathematicae, Tome 34 (2007) no. 4, pp. 493-503.

Résumé

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.

Détail

DOI : 10.4064/am34-4-8

Keywords: prove existence sequence satisfying sum nabla beta x x where function whose second order chet derivative nabla satifies center h lder condition set valued map banach space subsets banach space convergence method superquadratic