Light on the infinite group relaxation II: sufficient conditions for extremality, sequences, and algorithms
Author
Abstract
Suggested Citation
DOI: 10.1007/s10288-015-0293-8
Download full text from publisher
As the access to this document is restricted, you may want to search for a different version of it.
References listed on IDEAS
- Ralph Gomory, 2007. "The atoms of integer programming," Annals of Operations Research, Springer, vol. 149(1), pages 99-102, February.
- Valentin Borozan & Gérard Cornuéjols, 2009. "Minimal Valid Inequalities for Integer Constraints," Mathematics of Operations Research, INFORMS, vol. 34(3), pages 538-546, August.
- Balas, Egon & Jeroslow, Robert G., 1980. "Strengthening cuts for mixed integer programs," European Journal of Operational Research, Elsevier, vol. 4(4), pages 224-234, April.
- Egon Balas, 1971. "Intersection Cuts—A New Type of Cutting Planes for Integer Programming," Operations Research, INFORMS, vol. 19(1), pages 19-39, February.
- G. Dantzig & R. Fulkerson & S. Johnson, 1954. "Solution of a Large-Scale Traveling-Salesman Problem," Operations Research, INFORMS, vol. 2(4), pages 393-410, November.
- Santanu S. Dey & Jean-Philippe P. Richard, 2008. "Facets of Two-Dimensional Infinite Group Problems," Mathematics of Operations Research, INFORMS, vol. 33(1), pages 140-166, February.
- Egon Balas & Sebastián Ceria & Gérard Cornuéjols, 1996. "Mixed 0-1 Programming by Lift-and-Project in a Branch-and-Cut Framework," Management Science, INFORMS, vol. 42(9), pages 1229-1246, September.
- WOLSEY, Laurence A., 1975. "Faces for a linear inequality in 0-1 variables," LIDAM Reprints CORE 218, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, February.
- M. Grötschel & W. R. Pulleyblank, 1986. "Clique Tree Inequalities and the Symmetric Travelling Salesman Problem," Mathematics of Operations Research, INFORMS, vol. 11(4), pages 537-569, November.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
Cited by:
- Amitabh Basu & Michele Conforti & Marco Di Summa & Joseph Paat, 2019. "The Structure of the Infinite Models in Integer ProgrammingAbstract: The infinite models in integer programming can be described as the convex hull of some points or as the intersection of halfspaces ," Management Science, INFORMS, vol. 44(4), pages 1412-1430, November.
- Amitabh Basu & Michele Conforti & Marco Di Summa & Giacomo Zambelli, 2019. "Optimal Cutting Planes from the Group Relaxations," Management Science, INFORMS, vol. 44(4), pages 1208-1220, November.
Most related items
These are the items that most often cite the same works as this one and are cited by the same works as this one.- Amitabh Basu & Robert Hildebrand & Matthias Köppe, 2016. "Light on the infinite group relaxation I: foundations and taxonomy," 4OR, Springer, vol. 14(1), pages 1-40, March.
- Egon Balas, 2005. "Projection, Lifting and Extended Formulation in Integer and Combinatorial Optimization," Annals of Operations Research, Springer, vol. 140(1), pages 125-161, November.
- Kent Andersen & Gérard Cornuéjols & Yanjun Li, 2005. "Reduce-and-Split Cuts: Improving the Performance of Mixed-Integer Gomory Cuts," Management Science, INFORMS, vol. 51(11), pages 1720-1732, November.
- Egon Balas & Thiago Serra, 2020. "When Lift-and-Project Cuts Are Different," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 822-834, July.
- Aardal, K.I. & van Hoesel, S., 1995. "Polyhedral Techniques in Combinatorial Optimization," Other publications TiSEM ed028a07-eb6a-4c8d-8f21-d, Tilburg University, School of Economics and Management.
- Amitabh Basu & Robert Hildebrand & Matthias Köppe, 2015. "Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem. I. The One-Dimensional Case," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 105-129, February.
- Santanu S. Dey & Andrea Lodi & Andrea Tramontani & Laurence A. Wolsey, 2014. "On the Practical Strength of Two-Row Tableau Cuts," INFORMS Journal on Computing, INFORMS, vol. 26(2), pages 222-237, May.
- Amitabh Basu & Gérard Cornuéjols & François Margot, 2012. "Intersection Cuts with Infinite Split Rank," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 21-40, February.
- Anja Fischer & Frank Fischer, 2015. "An extended approach for lifting clique tree inequalities," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 489-519, October.
- Fatma Kılınç-Karzan, 2016. "On Minimal Valid Inequalities for Mixed Integer Conic Programs," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 477-510, May.
- Egon Balas & Gérard Cornuéjols & Tamás Kis & Giacomo Nannicini, 2013. "Combining Lift-and-Project and Reduce-and-Split," INFORMS Journal on Computing, INFORMS, vol. 25(3), pages 475-487, August.
- Amitabh Basu & Pierre Bonami & Gérard Cornuéjols & François Margot, 2011. "Experiments with Two-Row Cuts from Degenerate Tableaux," INFORMS Journal on Computing, INFORMS, vol. 23(4), pages 578-590, November.
- Sebastián Ceria, 2007. "A brief history of lift-and-project," Annals of Operations Research, Springer, vol. 149(1), pages 57-61, February.
- Michele Conforti & Gérard Cornuéjols & Giacomo Zambelli, 2011. "A Geometric Perspective on Lifting," Operations Research, INFORMS, vol. 59(3), pages 569-577, June.
- Gennadiy Averkov & Christian Wagner & Robert Weismantel, 2011. "Maximal Lattice-Free Polyhedra: Finiteness and an Explicit Description in Dimension Three," Mathematics of Operations Research, INFORMS, vol. 36(4), pages 721-742, November.
- Aardal, K. & van Hoesel, C.P.M., 1995. "Polyhedral techniques in combinatorial optimization," Research Memorandum 014, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- Valentin Borozan & Gérard Cornuéjols, 2009. "Minimal Valid Inequalities for Integer Constraints," Mathematics of Operations Research, INFORMS, vol. 34(3), pages 538-546, August.
- Matteo Fischetti & Domenico Salvagnin, 2013. "Approximating the Split Closure," INFORMS Journal on Computing, INFORMS, vol. 25(4), pages 808-819, November.
- Santanu S. Dey & Quentin Louveaux, 2011. "Split Rank of Triangle and Quadrilateral Inequalities," Mathematics of Operations Research, INFORMS, vol. 36(3), pages 432-461, August.
- William J. Cook & Daniel G. Espinoza & Marcos Goycoolea, 2010. "Generalized Domino-Parity Inequalities for the Symmetric Traveling Salesman Problem," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 479-493, May.
More about this item
Keywords
Cutting planes; Cut-generating functions; Minimal and extreme functions; Integer programming; Infinite group problem;All these keywords.
Statistics
Access and download statisticsCorrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:aqjoor:v:14:y:2016:i:2:d:10.1007_s10288-015-0293-8. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.