Relations between facets of low- and high-dimensional group problems
The paper studies facets of low- and high-dimensional infinite group problems which are important for deriving strong cutting planes for mixed integer programs. The authors aim to improve results obtained from one-dimensional groups by considering higher dimensional groups. They first review the group approach and prove some results that are used later to prove that certain functions are facet defining. They then introduce a sequential merge procedure, which allows to derive facets of general high-dimensional infinite group problems from facets of lower-dimensional group problems. Finally, they analyze the types of inequalities that can be generated for low-dimensional group problems using high-dimensional sequential merge group cuts.
scientific article; zbMATH DE number 5693208