Branch-and-cut for complementarity-constrained optimization

I. R. de Farias, E. Kozyreff, M. Zhao

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We report and analyze the results of our computational testing of branch-and-cut for the complementarity-constrained optimization problem (CCOP). Besides the MIP cuts commonly present in commercial optimization software, we used 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.

Original languageEnglish
Pages (from-to)365-403
Number of pages39
JournalMathematical Programming Computation
Issue number4
StatePublished - Dec 2014


  • Branch-and-cut
  • Complementarity
  • Knapsack set
  • Mixed-integer programming
  • Multiple-choice
  • Polyhedral method
  • Special ordered set


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