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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.
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Contributor : Célia Jean-Alexis Connect in order to contact the contributor
Submitted on : Tuesday, November 7, 2017 - 5:40:15 PM
Last modification on : Wednesday, July 18, 2018 - 8:11:27 PM


  • HAL Id : hal-01630560, version 1



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. ⟨hal-01630560⟩



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