Advances in Analysis

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DOI: 10.22606/aan.2017.24004

• Steeve Burnet
  Laboratoire LAMIA, EA4540, Université des Antilles, Département de Mathématiques et Informatique, Campus de Fouillole, 97159 Pointe-à-Pitre, France
• 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

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 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.

Set-valued mapping, generalized equations, semistability, superquadratic convergence, cubic convergence.

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