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Pré-Publication, Document De Travail Année : 2009

Certificates and relaxations for integer programming and the semi-group membership problem

Résumé

We consider integer programming and the semi-group membership problem. We provide the following theorem of the alternative: the system Ax=b has no nonnegative integral solution x if and only if p(b) <0 for some given polynomial p whose vector of coefficients lies in a convex cone that we characterize. We also provide a hierarchy of linear programming relaxations, where the continuous case Ax=b with x real and nonnegative, describes the first relaxation in the hierarchy.
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hal-00382774 , version 1 (11-05-2009)

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Jean-Bernard Lasserre, Eduardo S. Zeron. Certificates and relaxations for integer programming and the semi-group membership problem. 2009. ⟨hal-00382774⟩
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