Constrained Infinite Group Relaxations of MIPs Santanu

Recently minimal and extreme inequalities for continuous group relaxations of general mixed integer sets have been characterized. In this paper, we consider a stronger relaxation of general mixed integer sets by allowing constraints, such as bounds, on the free integer variables in the continuous group relaxation. We generalize a number of results for the continuous infinite group relaxation to this stronger relaxation and characterize the extreme inequalities when there are two integer variables. 1 Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium. E-mail: [email protected] 2 Université catholique de Louvain, CORE and INMA, B-1348 Louvain-la-Neuve, Belgium. E-mail: [email protected]. This author is also member of ECORE, the association between CORE and ECARES. We would like to thank Ellis Johnson for a motivating discussion and pointing out references [11] and [19]. We would also like to thank Amitabh Basu, Gerard Cornuéjols Michele Conforti, and Giacomo Zambelli for pointing out corrections to the statements of Proposition 2.1 and Proposition 6.3. This paper presents research results of the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian State, Prime Minister's Office, Science Policy Programming. The scientific responsibility is assumed by the authors.