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.
@article{arxiv.1507.05358,
title = {Another pedagogy for pure-integer Gomory},
author = {Qi He and Jon Lee},
journal= {arXiv preprint arXiv:1507.05358},
year = {2018}
}