Mathematical Programming Computation, Volume 6, Issue 4, December 2014

Branch-and-cut for complementarity-constrained optimization

Ismael R. de Farias Jr., Ernee Kozyreff, Ming Zhao

We report and analyze the results of our computational testing of branch-and-cut for the complementarity-constrained optimization problem (CCOP). Besides theMIP cuts commonly present in commercial optimization software,weused inequalities that explore complementarity constraints. To do so,we generalized two families of cuts proposed earlier by de Farias, Johnson, and Nemhauser that had never been tested computationally. Our test problems consisted of linear, binary, and general integer programs with complementarity constraints. Our results on the use of complementarity cuts within a major commercial optimization solver show that they are of critical importance to tackling difficult CCOP instances, typically reducing the computational time required to solve them tremendously.

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