Toward computer-assisted discovery and automated proofs of cutting plane theorems

TL;DR

This paper introduces a computer-assisted approach using metaprogramming and semialgebraic computations to prove both existing and novel theorems in the theory of cutting planes within Gomory--Johnson's model.

Contribution

It presents a novel method for automating proofs of cutting-plane theorems, combining metaprogramming with semialgebraic techniques.

Findings

Successfully proved classical and new cutting-plane theorems

Demonstrated the effectiveness of computer-assisted proofs in this domain

Enhanced understanding of cut generating functions

Abstract

Using a metaprogramming technique and semialgebraic computations, we provide computer-based proofs for old and new cutting-plane theorems in Gomory--Johnson's model of cut generating functions.