A class of multi-level balanced Foundation-Penalty cuts for mixed-integer programs

Glover and Sherali (2003) introduced a wide class of Foundation-Penalty (FP) cuts for GUB and ordinary mixed-integer programs. The FP cuts are easy to generate by exploiting routine branch-and-bound penalty calculations, and encompass other classical cuts such as disjunctive cuts, lift-and-project cuts, convexity cuts, Gomory cuts, and mixed-integer rounding cuts. Here we focus on two special classes of FP cuts, called balanced FP cuts and multi-level balanced FP cuts, and exhibit their relationship to special forms of disjunctive cuts. A numerical example illustrates the rich variety of cuts that can be generated.