@misc{AverkovConfortiDelPiaetal., author = {Averkov, Gennadiy and Conforti, Michelle and Del Pia, Alberto and Di Summa, Marco and Faenza, Yuri}, title = {On the convergence of the affine hull of the Chv{\´a}tal-Gomory closures}, series = {SIAM journal on discrete mathematics}, volume = {27}, journal = {SIAM journal on discrete mathematics}, number = {3}, issn = {1095-7146}, doi = {10.1137/120898371}, pages = {1492 -- 1502}, abstract = {Given an integral polyhedron \$P\subseteq\mathbb{R}^n\$ and a rational polyhedron \$Q\subseteq\mathbb{R}^n\$ containing the same integer points as \$P\$, we investigate how many iterations of the Chv{\´a}tal--Gomory closure operator have to be performed on \$Q\$ to obtain a polyhedron contained in the affine hull of \$P\$. We show that if \$P\$ contains an integer point in its relative interior, then such a number of iterations can be bounded by a function depending only on \$n\$. On the other hand, we prove that if \$P\$ is not full-dimensional and does not contain any integer point in its relative interior, then no finite bound on the number of iterations exists.}, language = {en} }