Hilbert basis (linear programming): Difference between revisions

Revision as of 08:34, 11 September 2011

Revision as of 10:02, 11 September 2011

Line 1:

In [[linear programming]], a '''Hilbert basis''' for a [[convex cone]] is an integer [[cone basis]]: minimal set of integer vectors such that every integer vector in the convex cone is a [[linear combination]] of the vectors in the Hilbert basis with non-negative integer coefficients.

== Definition ==

More precisely, aA set <math>\{a_1,\ldots,a_n\}</math> of integer vectors is a Hilbert basis if

every integer vector in its convex cone