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Partial Lagrangian relaxation for general quadratic programming

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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.

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Authors and Affiliations

  1. CEDRIC, CNAM-IIE, 18 allée Jean Rostand, 91025, Evry Cedex, France

    Alain Faye & Frédéric Roupin

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  1. Alain Faye
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  2. Frédéric Roupin
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Correspondence to Frédéric Roupin.

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Faye, A., Roupin, F. Partial Lagrangian relaxation for general quadratic programming. 4OR 5, 75–88 (2007). https://doi.org/10.1007/s10288-006-0011-7

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  • DOI: https://doi.org/10.1007/s10288-006-0011-7

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