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4OR

, Volume 5, Issue 1, pp 75–88 | Cite as

Partial Lagrangian relaxation for general quadratic programming

  • Alain Faye
  • Frédéric RoupinEmail author
Regular Paper

Abstract

We give a complete characterization of constant quadratic functions over an affine variety. This result is used to convexify the objective function of a general quadratic programming problem (Pb) which contains linear equality constraints. Thanks to this convexification, we show that one can express as a semidefinite program the dual of the partial Lagrangian relaxation of (Pb) where the linear constraints are not relaxed. We apply these results by comparing two semidefinite relaxations made from two sets of null quadratic functions over an affine variety.

Keywords

Quadratic programming Lagrangian relaxations Semidefinite programming 

MSC classification

90C20 90C22 

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.CEDRICCNAM-IIEEvry CedexFrance

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