Pith. sign in

REVIEW 1 cited by

Helly systems and certificates in optimization

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2111.05225 v3 pith:IMCLFBOI submitted 2021-11-09 math.OC cs.CC

Helly systems and certificates in optimization

classification math.OC cs.CC
keywords certificatesoptimizationgeneralhellypartsystemsapproachbehind
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
Share X Bluesky LinkedIn Reddit HN
read the original abstract

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 settings. We show that some important techniques existing in the literature are purely combinatorial in nature and do not depend on any underlying geometric notions.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Sample Complexity of Stochastic Optimization with Integer Variables

    cs.LG 2026-05 unverdicted novelty 7.0

    Stochastic integer optimization has sample complexity that matches, undercuts, or exceeds the continuous case based on objective structure, with new tight bounds for nonconvex continuous problems.