Monoidal cut strengthening and generalized mixed-integer rounding for disjunctions and complementarity constraints

In the early 1980s, Balas and Jeroslow presented monoidal disjunctive cuts exploiting the integrality of variables. This article investigates the relation of monoidal cut strengthening to other classes of cutting planes for general two-term disjunctions. We introduce a generalization of mixed-integer rounding cuts and show equivalence to monoidal disjunctive cuts. Moreover, we demonstrate the effectiveness of these cuts via computational experiments on instances involving complementarity constraints. Finally, we present an adaptation of the mixed-integer rounding approach for mixed-complementarity problems.