Split cuts for robust mixed-integer optimization

Robust optimization problems are conventionally solved by reformulation as non-robust problems. We propose a direct method to separate split cuts for robust mixed-integer programs with polyhedral uncertainty sets. The method generalizes the well-known cutting plane procedure of Balas. Computational experiments show that applying cutting planes directly is favorable to the reformulation approach. It is thus viable to solve robust MIP problems in a branch-and-cut framework using a generalized linear programming oracle.