An algorithm for mixed integer optimization

For many years the mathematical programming community has realized the practical importance of developing algorithmic tools for tackling mixed integer optimization problems. Given our ability to solve linear optimization problems efficiently, one is inclined to think that a mixed integer program with both continuous and discrete variables is easier than a pure integer programming problem since integrality on the variables is required for a subset of the variables only. This however is not true at all. In fact, a second view towards a mixed integer program shows that themixture of continuous and discrete components causes a significant increase in complexity with respect to geometric, algebraic, combinatorial and algorithmic properties. In this light it is not too surprising that not only the derivation of cutting planes for a mixed integer program is more involved than in the pure integer setting, but also that there is no finite cutting plane algorithm known for general mixed