Helly numbers of subsets of ℝᵈ and sampling techniques in optimization

@inproceedings{Loera2015HellyNO,
  title={Helly numbers of subsets of ℝᵈ and sampling techniques in optimization},
  author={Jes{\'u}s A. De Loera and Reuben N. La Haye and Deborah Oliveros and Edgardo Rold{\'a}n-Pensado},
  year={2015}
}
We present Helly-type theorems where the convex sets are required to intersect a subset S of R d . This is a continuation of prior work for S = R d , Z d , and Z d k R k (motivated by mixed-integer optimization). We are particularly interested in the case when S has some algebraic structure, in particular when S is a subgroup or the dierence between a lattice and some sublattices. We give sharp bounds on the Helly numbers for S in several cases. By abstracting the ingredients of a general… CONTINUE READING

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