A proof of Lovász's theorem on maximal lattice-free sets

Details A proof of Lovász's theorem on maximal lattice-free sets A proof of Lovász's theorem on maximal lattice-free sets

2011-10-05

arxiv.org/abs/1110.1014v1

Mathematics

Optimization and Control

Scientific paper

Let $K$ be a maximal lattice-free set in $\mathbb{R}^d$, that is, $K$ is convex and closed subset of $\mathbb{R}^d$, the interior of $K$ does not cointain points of $\mathbb{Z}^d$ and $K$ is inclusion-maximal with respect to the above properties. A result of Lov\'asz assert that if $K$ is $d$-dimensional, then $K$ is a polyhedron with at most $2^d$ facets, and the recession cone of $K$ is spanned by vectors from $\mathbb{Z}^d$. A first complete proof of mentioned Lov\'asz's result has been published in a paper of Basu, Conforti, Cornu\'ejols and Zambelli (where the authors use Dirichlet's approximation as a tool). The aim of this note is to give another proof of this result. Our proof relies on Minkowki's first fundamental theorem from the gemetry of numbers. We remark that the result of Lov\'asz is relevant in integer and mixed-integer optimization.

Affiliated with

Also associated with

No associations

Rating

A proof of Lovász's theorem on maximal lattice-free sets does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A proof of Lovász's theorem on maximal lattice-free sets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A proof of Lovász's theorem on maximal lattice-free sets will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-325730