TY - GEN A1 - Averkov, Gennadiy A1 - Conforti, Michelle A1 - Del Pia, Alberto A1 - Di Summa, Marco A1 - Faenza, Yuri T1 - On the convergence of the affine hull of the Chvátal-Gomory closures T2 - SIAM journal on discrete mathematics N2 - 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 Chvátal--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. KW - affine hul KW - Chvátal–Gomory closure KW - Chvátal rank KW - cutting plane KW - integral polyhe-dron Y1 - 2013 UR - https://epubs.siam.org/doi/10.1137/120898371 U6 - https://doi.org/10.1137/120898371 SN - 1095-7146 SN - 0895-4801 VL - 27 IS - 3 SP - 1492 EP - 1502 ER - TY - GEN A1 - Averkov, Gennadiy T1 - On finitely generated closures in the theory of cutting planes T2 - Discrete optimization KW - Chvátal–Gomory closure KW - Cutting plane KW - Max-facet-width KW - Mixed-integer optimization KW - Split closure Y1 - 2012 UR - https://www.sciencedirect.com/science/article/pii/S1572528612000436?via%3Dihub U6 - https://doi.org/10.1016/j.disopt.2012.06.003 SN - 1572-5286 VL - 9 IS - 4 SP - 209 EP - 215 ER -