A Second-Order Bundle Method to Minimize the Maximum Eigenvalue Function

François Oustry 1
1 NUMOPT - Numerical Optimization
Inria Grenoble - Rhône-Alpes
Abstract : In this paper we present a nonsmooth algorithm to minimize the maximum eigenvalue of matrices belonging to an affine subspace of n x n symmetric matrices. We show how a simple bundle method, the approximate eigenvalue method can be used to globalize the second-order method developed by M. L. Overton in the eighties and recently revisited in the framework of the U-Lagrangian theory. With no additional assumption, the resulting algorithm generates a minimizing sequence. A geometrical and constructive proof is given. To prove that quadratic convergence is achieved asymptotically- , some strict complementarity and non-degeneracy assumptions are needed. We also introduce a new generation of bundle methods for semidefinite programming.
Type de document :
Rapport
RR-3738, INRIA. 1999
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https://hal.inria.fr/inria-00072927
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Soumis le : mercredi 24 mai 2006 - 11:17:49
Dernière modification le : mercredi 11 avril 2018 - 01:51:33
Document(s) archivé(s) le : dimanche 4 avril 2010 - 23:27:59

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François Oustry. A Second-Order Bundle Method to Minimize the Maximum Eigenvalue Function. RR-3738, INRIA. 1999. 〈inria-00072927〉

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