Pseudopower expansion of solutions of generalized equations and constrained optimization problems

1 PROMATH - Mathematical Programming
Inria Paris-Rocquencourt
Abstract : We compute the solution of a strongly regular perturbed generalized equations as the sum of a speudopower expansion, i.e. the expansion at order k is the solution of the generalized equation expanded at order k and thus depends itself on the perturbation parameter [??]. In the polyhedral case, the pseudopower expansion reduces to a classical Taylor expansion. For constrained optimization problems with strongly regular solution, we check that the quadratic growth condition holds and that, at least locally, solutions of the problem and solutions of the associated optimality system coincide. In the special case of a finite number of inequality constraints, the solution and the Lagrange multiplier can be expanded in Taylor series if the gradients of the active constraints are linearly independent. If the data are analytic, the solution and the multiplier are analytic functions in [??] provided that some strong second order condition holds.
Type de document :
Rapport
[Research Report] RR-1956, INRIA. 1993
Domaine :

https://hal.inria.fr/inria-00074717
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Soumis le : mercredi 24 mai 2006 - 16:08:00
Dernière modification le : vendredi 25 mai 2018 - 12:02:05
Document(s) archivé(s) le : mardi 12 avril 2011 - 18:28:24

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• HAL Id : inria-00074717, version 1

Citation

J. Frederic Bonnans. Pseudopower expansion of solutions of generalized equations and constrained optimization problems. [Research Report] RR-1956, INRIA. 1993. 〈inria-00074717〉

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