This paper analyses the feasible sets structure of general mixed integer linear programs (MIPs) and its relationship with the existence of a finite cardinality test set which can be applied in augmentation algorithms. We derive and characterize a computable, finite test set for MIPs which can be embedded in a finite augmentation algorithm. Several examples illustrate the structure of this set and its relationship with previous approaches in the literature.
@article{arxiv.2507.08525,
title = {Augmentation approaches for Mixed Integer Programming},
author = {Justo Puerto and Jose A. Ruiz-Alba},
journal= {arXiv preprint arXiv:2507.08525},
year = {2025}
}