Hilbert basis (linear programming): Difference between revisions

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:<math> x=\lambda_1 x_1+\ldots+\lambda_m x_m, \quad\lambda_1,\ldots,\lambda_m\in\mathbb{Z}, \lambda_1,\ldots,\lambda_m\geq0</math>

The '''Hilbert basis''' ofcone ''C'' is thecalled pointed, if <math>x,-x\in C</math> implies <math>x=0</math>. In this case there exists a unique minimal generating set of the monoid <math>C\cap L</math> - the '''Hilbert basis''' of ''C''. It is given by set of irreducible lattice points: An element <math>x\in C\cap L</math> is called irreducible if it can not be written as the sum of two non-zero elements, i.e., <math>x=y+z</math> implies <math>y=0</math> or <math>z=0</math>.

== References ==