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Reports Year : 1999

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

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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Dates and versions

inria-00072927 , version 1 (24-05-2006)

Identifiers

  • HAL Id : inria-00072927 , version 1

Cite

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