64 citations · 418 across the 52 of their papers we have counts for
4 papers · 1 filter
Helly numbers of Algebraic Subsets of
J. A. De Loera, R. N. La Haye, D. Oliveros +1
We study -convex sets, which are the geometric objects obtained as the intersection of the usual convex sets in with a proper subset . We con…
Helly's Theorem: New Variations and Applications
Nina Amenta, Jesús A. De Loera, Pablo Soberón
This survey presents recent Helly-type geometric theorems published since the appearance of the last comprehensive survey, more than ten years ago. We discuss how such theorems con…
Beyond Chance-Constrained Convex Mixed-Integer Optimization: A Generalized Calafiore-Campi Algorithm and the notion of -optimization
J. A. De Loera, R. N. La Haye, D. Oliveros +1
The scenario approach developed by Calafiore and Campi to attack chance-constrained convex programs utilizes random sampling on the uncertainty parameter to substitute the original…
Random Sampling in Computational Algebra: Helly Numbers and Violator Spaces
Jesús A. De Loera, Sonja Petrović, Despina Stasi
This paper transfers a randomized algorithm, originally used in geometric optimization, to computational problems in commutative algebra. We show that Clarkson's sampling algorithm…