Helly systems and certificates in optimization [article]

Amitabh Basu, Tongtong Chen, Michele Conforti, Hongyi Jiang
2022 arXiv   pre-print
Inspired by branch-and-bound and cutting plane proofs in mixed-integer optimization and proof complexity, we develop a general approach via Hoffman's Helly systems. This helps to distill the main ideas behind optimality and infeasibility certificates in optimization. The first part of the paper formalizes the notion of a certificate and its size in this general setting. The second part of the paper establishes lower and upper bounds on the sizes of these certificates in various different
more » ... s. We show that some important techniques existing in the literature are purely combinatorial in nature and do not depend on any underlying geometric notions.
arXiv:2111.05225v3 fatcat:elfvauedlrd47ogpg22vr4tdm4