Abstract
We give an algorithm for testing the extremality of a large class of minimal valid functions for the two-dimensional infinite group problem.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Basu, A., Hildebrand, R., Köppe, M.: Equivariant perturbation in Gomory and Johnson’s infinite group problem. eprint arXiv:1206.2079 (math.OC) (2012)
Basu, A., Hildebrand, R., Köppe, M., Molinaro, M.: A (k + 1)-slope theorem for the k-dimensional infinite group relaxation. eprint arXiv:1109.4184 (math.OC) (2011)
Cornuéjols, G., Molinaro, M.: A 3-slope theorem for the infinite relaxation in the plane. Mathematical Programming, 1–23 (2012), doi:10.1007/s10107-012-0562-7
Dey, S.S., Richard, J.-P.P.: Facets of two-dimensional infinite group problems. Mathematics of Operations Research 33(1), 140–166 (2008)
Dey, S.S., Richard, J.-P.P.: Relations between facets of low- and high-dimensional group problems. Mathematical Programming 123(2), 285–313 (2010)
Dey, S.S., Richard, J.-P.P., Li, Y., Miller, L.A.: On the extreme inequalities of infinite group problems. Mathematical Programming 121(1), 145–170 (2009)
Gomory, R.E.: Some polyhedra related to combinatorial problems. Linear Algebra and its Applications 2(4), 451–558 (1969)
Gomory, R.E., Johnson, E.L.: Some continuous functions related to corner polyhedra, I. Mathematical Programming 3, 23–85 (1972), doi:10.1007/BF01585008
Gomory, R.E., Johnson, E.L.: Some continuous functions related to corner polyhedra, II. Mathematical Programming 3, 359–389 (1972), doi:10.1007/BF01585008
Gomory, R.E., Johnson, E.L.: T-space and cutting planes. Mathematical Programming 96, 341–375 (2003), doi:10.1007/s10107-003-0389-3
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Basu, A., Hildebrand, R., Köppe, M. (2013). Equivariant Perturbation in Gomory and Johnson’s Infinite Group Problem: II. The Unimodular Two-Dimensional Case. In: Goemans, M., Correa, J. (eds) Integer Programming and Combinatorial Optimization. IPCO 2013. Lecture Notes in Computer Science, vol 7801. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36694-9_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-36694-9_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36693-2
Online ISBN: 978-3-642-36694-9
eBook Packages: Computer ScienceComputer Science (R0)