Four decades ago, Gomory introduced the corner polyhedron as a relaxation of a mixed
integer set in tableau form and Balas introduced intersection cuts for the corner polyhedron …

While many classes of cutting-planes are at the disposal of integer programming solvers, our
scientific understanding is far from complete with regards to cutting-plane selection, ie, the …

We study the generalization of split, k-branch split, and intersection cuts from mixed integer
linear programming to the realm of mixed integer nonlinear programming. Constructing such …

In Chaps. 5 and 6 we have introduced several classes of valid inequalities that can be used
to strengthen integer programming formulations in a cutting plane scheme. All these valid …

In this paper we study the relationship between valid inequalities for mixed-integer sets,
lattice-free sets associated with these inequalities and the multi-branch split cuts introduced …

We develop a method for computing facet-defining valid inequalities for any mixed-integer
set P_J PJ. While our practical implementation does not return only facet-defining …

In this paper, we study whether cuts obtained from two simplex tableau rows at a time can
strengthen the bounds obtained by Gomory mixed-integer (GMI) cuts based on single …

Split cuts form a well-known class of valid inequalities for mixed-integer programming
problems. Cook et al.(Math Program 47: 155–174, 1990) showed that the split closure of a …

We address the issue of generating cutting planes for mixed integer programs from multiple
rows of the simplex tableau with the tools of disjunctive programming. A cut from q rows of …

Split cuts are among the most important and well-understood cuts for general mixed-integer
programs. In this paper we consider some recent generalizations of split cuts and compare …