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inria-00073709, version 1

Sensitivity Analysis of Optimization Problems under Second Order Regular Constraints

J. Frederic Bonnans () 1, Roberto Cominetti, Alexander Shapiro

N° RR-2989 (1996)

Résumé : We present a perturbation theory for finite dimensional optimization problems subject to abstract constraints satisfying a second order regularity condition. We derive Lipschitz and Hölder expansions of approximate optimal solutions, under a directional constraint qualification hypothesis and various second order sufficient conditions that take into account the curvature of the set defining the constraints of the problem. We also show how the theory applies to semi-definite optimization and, more generally, to semi-infinite programs in which the contact set is a smooth manifold and the quadratic growth condition in the constraint space holds. As a final application we provide a result on differentiability of metric projections in finite dimensional spaces.

  • 1 :  PROMATH (INRIA Rocquencourt)
  • INRIA
  • Domaine : Informatique/Autre
    Mathématiques/Optimisation et contrôle
  • Mots-clés : SENSITIVITY ANALYSIS / PARAMETRIC OPTIMIZATION / OPTIMAL VALUE FUNCTION / DIRECTIONAL CONSTRAINT QUALIFICATION / SECOND ORDER OPTIMALITY CONDITIONS / SEMI-DEFINITE PROGRAMMING / SEMI-INFINITE PROGRAMMING / METRIC PROJECTION / DIRECTIONAL DIFFERENTIABILITY
  • Référence interne : RR-2989
  • Commentaire : Projet PROMATH
 
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  • Soumis le : Mercredi 24 Mai 2006, 13:34:35
  • Dernière modification le : Mercredi 18 Juillet 2007, 11:59:15