Branch-and-Cut for Complementarity and Cardinality Constrained Linear Programs

A complementarity constraint requires that at most one of two variables is nonzero and a cardinality constraint enforces an upper bound on the number of nonzero variables of a certain set. In this thesis, we investigate a branch-and-cut algorithm to solve linear programs with complementarity and cardinality constraints. We focus on the case in which the complementarity and cardinality constraints overlap, i.e., share variables. The corresponding conflict hypergraph can algorithmically be exploited, for instance, for improved branching rules, preprocessing, primal heuristics, and cutting planes. In an extensive computational study, we evaluate the components of our implementation on instances of different applications. We also demonstrate the effectiveness of this approach by comparing it to the solution of a mixed-integer programming formulation, if the variables appearing in the complementarity and cardinality constraints are bounded.