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Une Methode de Quasi-Newton Reduite en Optimisation Sous Contraintes Avec Priorite a la Restauration

  • Jean Charles Gilbert
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 83)

Résumé

Pour minimiser une fonction sur Rn en présence de m contraintes d’égalité non linéaires, on propose un algorithme ayant les caractéristiques suivantes: chaque itération comprend deux pas de restauration des contraintes et un pas de minimisation de la fonction, les contraintes sont linéairisées une fois par itération, une matrice d’ordre n-m (approximation du hessien réduit du lagrangien) est mise jour mais pas à chaque itération (un critère de mise à jour est proposé), la méthode est globale avec priorité à la restauration, enfin, la suite de points générée converge Q-superlinéairement.

Abstract

To minimize a function on Rn withm nonlinear equality constraints, we propose an algorithm with the following features: each iteration is formed of two steps of restoration of the constraints and one step of minimization of the function, the constraints are linearized once per iteration, a matrix of order n-m (approximation of the reduced hessian of the lagrangian) is updated but not at each iteration (a criterion is proposed), the method is global with priority to the restoration and generates a Q-superlinearlyconvergingsequence of points.

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Copyright information

© Springer Science+Business Media Dordrecht 1986

Authors and Affiliations

  • Jean Charles Gilbert
    • 1
  1. 1.boursier scientifique et technique de la Commission des Communautés EuropéennesCentre d’Etudes Nucléaires (D.R.F.C.)Fontenay-aux-Roses CedexFrance

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