Paper Info
Title
Light on the infinite group relaxation II: sufficient conditions for extremality, sequences, and algorithms
Abstract
This is the second part of a survey on the infinite group problem, an infinite-dimensional relaxation of integer linear optimization problems introduced by Ralph Gomory and Ellis Johnson in their groundbreaking papers titled Some continuous functions related to corner polyhedra I, II (Math Program 3:23–85, 1972a; Math Program 3:359–389, 1972b). The survey presents the infinite group problem in the modern context of cut generating functions. It focuses on the recent developments, such as algorithms for testing extremality and breakthroughs for the k-row problem for general \(k\ge 1\) that extend previous work on the single-row and two-row problems. The survey also includes some previously unpublished results; among other things, it unveils piecewise linear extreme functions with more than four different slopes. An interactive companion program, implemented in the open-source computer algebra package Sage, provides an updated compendium of known extreme functions.
Year
DOI
Venue
2016
10.1007/s10288-015-0293-8
4OR
Keywords
Field
DocType
Cutting planes, Cut-generating functions, Minimal and extreme functions, Integer programming, Infinite group problem
Integer,Discrete mathematics,Generating function,Mathematical optimization,Infinite group,Polyhedron,Symbolic computation,Algorithm,Integer programming,Linear programming,Piecewise linear function,Mathematics
Journal
Volume
Issue
ISSN
14
2
1614-2411
Citations 
PageRank 
References 
11
0.62
47
Authors
3
Name
Order
Citations
PageRank
Amitabh Basu133127.36
robert hildebrand2131.00
Matthias KöPpe319120.95