3 papers
math.OC2025
Geoffrion's theorem beyond finiteness and rationality
Santanu S. Dey, Frédéric Meunier, Diego Moran Ramirez
Geoffrion's theorem is a fundamental result from mathematical programming assessing the quality of Lagrangian relaxation, a standard technique to get bounds for integer programs. A…
math.CO2025
Colorful circuits and colorful topes in oriented matroids
Minho Cho, Seunghun Lee, Frédéric Meunier
We provide a short proof of a conic version of the colorful Carathéodory theorem for oriented matroids. Holmsen's extension of the colorful Carathéodory theorem to oriented matroid…
math.CO2025
Matroids, intersecting bases, and Borsuk property
Gyivan López-Campos, Frédéric Meunier, Jorge L. Ramírez Alfonsín
A subset of has the Borsuk property if it can be decomposed into at most parts of diameter smaller than . This is an important geometric property, inspir…