Exact and inexact Hummel-Seebeck method for variational inclusions

Abstract : 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.
Type de document :
Article dans une revue
advances in analysis, 2017, 2 (4), pp.257-266. 〈10.22606〉
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https://hal.archives-ouvertes.fr/hal-01630560
Contributeur : Célia Jean-Alexis <>
Soumis le : mardi 7 novembre 2017 - 17:40:15
Dernière modification le : mercredi 18 juillet 2018 - 20:11:27

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  • HAL Id : hal-01630560, version 1
  • DOI : 10.22606

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Steve Burnet, Célia Jean-Alexis, Alain Piétrus. Exact and inexact Hummel-Seebeck method for variational inclusions. advances in analysis, 2017, 2 (4), pp.257-266. 〈10.22606〉. 〈hal-01630560〉

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