Exact and Inexact Hummel-Seebeck Type Method for Variational Inclusions
Laboratoire LAMIA, EA4540, Université des Antilles, Département de Mathématiques et Informatique, Campus de Fouillole, 97159 Pointe-à-Pitre — France, Steeve Burnet, Célia Jean-Alexis, Laboratoire LAMIA, EA4540, Université des Antilles, Département de Mathématiques et Informatique, Campus de Fouillole, 97159 Pointe-à-Pitre — France, Alain Piétrus, Laboratoire LAMIA, EA4540, Université des Antilles, Département de Mathématiques et Informatique, Campus de Fouillole, 97159 Pointe-à-Pitre — France · Advances in Analysis · 2017
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 R n to the closed subsets of R n .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.