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Optimal cutting planes from the group relaxations

Basu, Amitabh, Conforti, Michele, Di Summa, Marco and Zambelli, Giacomo (2019) Optimal cutting planes from the group relaxations. Mathematics of Operations Research, 44 (4). pp. 1208-1220. ISSN 0364-765X

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Identification Number: 10.1287/moor.2018.0964


We study quantitative criteria for evaluating the strength of valid inequalities for Gomory and Johnson's finite and infinite group models and we describe the valid inequalities that are optimal for these criteria. We justify and focus on the criterion of maximizing the volume of the nonnegative orthant cut off by a valid inequality. For the finite group model of prime order, we show that the unique maximizer is an automorphism of the Gomory Mixed-Integer (GMI) cut for a possibly different finite group problem of the same order. We extend the notion of volume of a simplex to the infinite dimensional case. This is used to show that in the infinite group model, the GMI cut maximizes the volume of the nonnegative orthant cut off by an inequality.

Item Type: Article
Official URL:
Additional Information: © 2019 INFORMS
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 17 Aug 2018 15:37
Last Modified: 20 Oct 2021 01:28
Projects: CMMI1452820, SID 2016, PRIN 2016
Funders: National Science Foundation

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