Dabeen Lee (이다빈), On a generalization of the Chvátal-Gomory closure

Integer programming is the problem of optimizing a linear function over the set of integer solutions satisfying a system of inequalities. The most successful technique in practice is the so-called “cutting-plane” algorithm in combination with branch-and-bound enumeration. Cutting-planes for an integer linear program are linear inequalities that are valid for all integer feasible solutions but cut off intermediate fractional solutions.

The Chvátal-Gomory cuts, introduced by Gomory in 1958 and further studied by Chvátal in 1973 in relation to their applications in combinatorial optimization, are the first class of general-purpose cutting-planes in the literature. The split cuts, whose name was coined by Cook, Kannan, and Schrijver in 1980, are another class of important cutting-planes in modern integer programming. Although there are infinitely many cuts in each class, it is known that only finitely many of them are nonredundant, which is related to designing a finite-convergent cutting-plane algorithm. In this talk, we introduce a new class of cutting-planes that generalizes the Chvátal-Gomory cuts and generalizes a special case of the split cuts. As the two classic classes of cutting-planes, we show that only a finite number of cuts can be redundant.

This talk is based on a joint work with Sanjeeb Dash and Oktay Günlük.