Hilbert basis (linear programming)

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In linear programming, a Hilbert basis for a convex cone C is an integer cone basis: minimal set of integer vectors such that every integer vector in C is a conical combination of the vectors in the Hilbert basis with integer coefficients.

Definition

A set of integer vectors is a Hilbert basis of its convex cone

if every integer vector from C belongs to the integer convex cone of A:

and no vector from A belongs to the integer convex cone of the others.

References

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