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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.
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Submitted on : Wednesday, May 24, 2006 - 11:17:49 AM
Last modification on : Friday, February 4, 2022 - 3:23:53 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:27:59 PM


  • HAL Id : inria-00072927, version 1



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



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