Face Dimensions of General-Purpose Cutting Planes for Mixed-Integer Linear Programs

用于割平面的新型序列无关提升技术及其诱导面的条件

New Sequence-Independent Lifting Techniques for Cutting Planes and When They Induce Facets

该研究推广并修正了GNS序列无关提升方法，提出可定义面的分段常数（PC）提升技术，验证其可作为GNS提升的有效替代，配套覆盖割生成程序在CPLEX实验中表现良好。

Algorithmic and Complexity Results for Cutting Planes Derived from Maximal Lattice-Free Convex Sets

We study a mixed integer linear program with m integer variables and k non-negative continuous variables in the form of the relaxation of the corner polyhedron that was introduced by Andersen, Louveaux, Weismantel and Wolsey [Inequalities from two rows of a simplex tableau, Proc. IPCO 2007, LNCS, vol. 4513, Springer, pp. 1--15]. We describe the facets of this mixed integer linear program via the extreme points of a well-defined polyhedron. We then utilize this description to give polynomial time algorithms to derive valid inequalities with optimal l_p norm for arbitrary, but fixed m. For the c…

Improved theoretical guarantees regarding a class of two-row cutting planes

The corner polyhedron is described by minimal valid inequalities from maximal lattice-free convex sets. For the Relaxed Corner Polyhedron (RCP) with two free integer variables and any number of non-negative continuous variables, it is known that such facet defining inequalities arise from maximal lattice-free splits, triangles and quadrilaterals. We improve on the tightest known upper bound for the approximation of the RCP, purely by minimal valid inequalities from maximal lattice-free quadrilaterals, from 2 to 1.71. We generalize the tightest known lower bound of 1.125 for the approximation o…

The Triangle Closure is a Polyhedron

Recently, cutting planes derived from maximal lattice-free convex sets have been studied intensively by the integer programming community. An important question in this research area has been to decide whether the closures associated with certain families of lattice-free sets are polyhedra. For a long time, the only result known was the celebrated theorem of Cook, Kannan and Schrijver who showed that the split closure is a polyhedron. Although some fairly general results were obtained by Andersen, Louveaux and Weismantel [ An analysis of mixed integer linear sets based on lattice point free co…