Éditeur(s) : HAL CCSD Tsing Hua University
Résumé : International audience
This paper deals with variational inclusions of the form : $0in varphi(z)+F(z)$ where $varphi$ is a single-valued function admitting a second order Fréchet derivative and $F$ is a set-valued map from $R^q$ to the closed subsets of $R^q$. In order to approximate a solution $bar z$ of the previous inclusion, we use an iterative scheme based on a multipoint method. We obtain, thanks to some semistability properties of $bar z$, local superquadratic or cubic convergent sequences
ISSN: 1607-2510

hal-00728816
https://hal.archives-ouvertes.fr/hal-00728816

Éditeur(s) : HAL CCSD
Résumé : International audience
We deal with a perturbed version of a Hummel-Seebeck type method to approximate a solution of variational inclusions of the form : 0 ∈ Φ(z) + F(z) where Φ is a single-valued function twice continuously Fréchet differentiable and F is a set-valued map from Rn to the closed subsets of Rn. This framework is convenient to treat in a unified way standard sequential quadratic programming, its stabilized version, sequential quadratically constrained quadratic programming, and linearly constrained Lagrangian methods (see [1]). We obtain, thanks to some semistability and another property (which is close to the hemistability) of the solution z ̄ of the previous inclusion, the local existence of a sequence that is superquadratically or cubically convergent.
ISSN: 2518-3680

hal-01630560
https://hal.archives-ouvertes.fr/hal-01630560
DOI : 10.22606

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
The aim of this study is the approximation of a solution x* of a ganeralized equation 0 in f(x)+F(x) in Banach spaces, where f is a single-valued function whose second order Frechet derivative satisfies an Hölder condition and F stands for a set-valed map with closed graph. Using a fixed point theorem and the Aubin property of F, we show the existence and the superquadratic convergence of a sequence derived from a midpoint method.
ISSN: 0167-8019

hal-00642118
https://hal.archives-ouvertes.fr/hal-00642118