Abstract
In this paper we explore the geometry of the integer points in a cone rooted at a rational point. This basic geometric object allows us to establish some links between lattice point free bodies and the derivation of inequalities for mixed integer linear programs by considering two rows of a simplex tableau simultaneously.
This work was partly carried out within the framework of ADONET, a European network in Algorithmic Discrete Optimization, contract no. MRTN-CT-2003-504438. The second author is supported by FRS-FNRS. This text presents research results of the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian State, Prime Minister’s Office, Science Policy Programming. The scientific responsibility is assumed by the authors.
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References
Arkinstall, J.R.: Minimal requirements for Minkowski’s theorem in the plane I. Bulletin of the Australian Mathematical Society 22, 259–274 (1980)
Balas, E.: Intersection cuts - a new type of cutting planes for integer programming. Operations Research 19, 19–39 (1971)
Cook, W.J., Kannan, R., Schrijver, A.: Chvátal closures for mixed integer programming problems. Mathematical Programming 47, 155–174 (1990)
Gomory, R.E.: An algorithm for the mixed integer problem. Technical Report RM-2597, The Rand Corporation (1960a)
Johnson, E.: On the group problem for mixed integer programming. Mathematical Programming 2, 137–179 (1974)
Nemhauser, G.L., Wolsey, L.A.: Integer and combinatorial optimization. Wiley, Chichester (1988)
Rabinowitz, S.: A census of convex lattice polygons with at most one interior lattice point. Ars Combinatoria 28, 83–96 (1989)
Schrijver, A.: Theory of linear and integer programming. Wiley, Chichester (1986)
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Andersen, K., Louveaux, Q., Weismantel, R., Wolsey, L.A. (2007). Inequalities from Two Rows of a Simplex Tableau. In: Fischetti, M., Williamson, D.P. (eds) Integer Programming and Combinatorial Optimization. IPCO 2007. Lecture Notes in Computer Science, vol 4513. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72792-7_1
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DOI: https://doi.org/10.1007/978-3-540-72792-7_1
Publisher Name: Springer, Berlin, Heidelberg
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