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Journal of Global Optimization

, Volume 44, Issue 1, pp 1–28 | Cite as

Local minima of quadratic forms on convex cones

  • Alberto SeegerEmail author
  • Mounir Torki
Article

Abstract

We study the local minima and the critical values of a quadratic form on the trace of a convex cone. This variational problem leads to the development of a spectral theory that combines matrix algebra and facial analysis of convex cones.

Keywords

Convex cones Conic quadratic programming Linear complementarity problems Cone-constrained eigenvectors 

Mathematics Subject Classifications

15A18 58C40 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of AvignonAvignonFrance
  2. 2.University of Avignon, I.U.P.AvignonFrance

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