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Theses

Contribution à la sensibilité et à la stabilité en optimisation et en théorie métrique des points critiques

Abstract : In this thesis, we propose some contributions to variational analysis in metric spaces and to optimization: metric regularity, metric critical point theory, sensitivity of Hoffman constants, stability in quadratic programming. In the polyhedral case, we establish explicit formulae for Hoffman constants of polyhedrons with explicit equalities. As these constants, under some regularity conditions, have a Lipschitzian behaviour, we calculate then the Clarke subdifferential of the associated functions. We also make a review of the metric regularity of multifunctions, and we treat some questions of stability in convex quadratic programming. The consideration of the notion of weak slope, and thus of appropriate deformation tools, allows us to establish results on the homotopical stability of isolated critical points of continuous functions on metric spaces.
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https://tel.archives-ouvertes.fr/tel-00004094
Contributor : Abderrahim Hantoute <>
Submitted on : Monday, January 5, 2004 - 7:20:11 PM
Last modification on : Friday, January 10, 2020 - 9:08:06 PM
Long-term archiving on: : Wednesday, September 12, 2012 - 12:15:29 PM

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  • HAL Id : tel-00004094, version 1

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Abderrahim Hantoute. Contribution à la sensibilité et à la stabilité en optimisation et en théorie métrique des points critiques. Mathématiques [math]. Université Paul Sabatier - Toulouse III, 2003. Français. ⟨tel-00004094⟩

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