A note on the MIR closure and basic relaxations of polyhedra

Anderson, Cornuejols and Li (2005) show that for a polyhedral mixed integer set defined by a constraint system Ax >= b, where x is n-dimensional, along with integrality restrictions on some of the variables, any split cut is in fact a split cut for a “basic relaxation”, i.e., one defined by a subset of linearly … Read more

Valid inequalities based on the interpolation procedure

We study the interpolation procedure of Gomory and Johnson (1972), which generates cutting planes for general integer programs from facets of master cyclic group polyhedra. This idea has recently been re-considered by Evans (2002) and Gomory, Johnson and Evans (2003). We compare inequalities generated by this procedure with mixed-integer rounding (MIR) based inequalities discussed in … Read more