Another pedagogy for pure-integer Gomory

TL;DR

This paper introduces a new approach to pure-integer Gomory cuts by deriving them from a dual form and applying them as columns in the primal problem, resulting in a finitely-terminating algorithm.

Contribution

It presents a novel method for generating pure-integer Gomory cuts using the primal simplex algorithm and a dual form approach, differing from traditional methods.

Findings

Finitely-terminating pure-integer Gomory cuts

Application of cuts as columns in the primal problem

Use of primal simplex algorithm for cut derivation

Abstract

We present pure-integer Gomory cuts in a way so that they are derived with respect to a "dual form" pure-integer optimization problem and applied on the standard-form primal side as columns, using the primal simplex algorithm. The input integer problem is not in standard form, and so the cuts are derived a bit differently. In this manner, we obtain a finitely-terminating version of pure-integer Gomory cuts that employs the primal rather than the dual simplex algorithm.