TY - GEN

T1 - On some generalizations of the split closure

AU - Dash, Sanjeeb

AU - Günlük, Oktay

AU - Ramirez, Diego Alejandro Morán

PY - 2013

Y1 - 2013

N2 - Split cuts form a well-known class of valid inequalities for mixed-integer programming problems (MIP). Cook et al. (1990) showed that the split closure of a rational polyhedron P is again a polyhedron. In this paper, we extend this result from a single rational polyhedron to the union of a finite number of rational polyhedra. We also show how this result can be used to prove that some generalizations of split cuts, namely cross cuts, also yield closures that are rational polyhedra.

AB - Split cuts form a well-known class of valid inequalities for mixed-integer programming problems (MIP). Cook et al. (1990) showed that the split closure of a rational polyhedron P is again a polyhedron. In this paper, we extend this result from a single rational polyhedron to the union of a finite number of rational polyhedra. We also show how this result can be used to prove that some generalizations of split cuts, namely cross cuts, also yield closures that are rational polyhedra.

KW - Cross cuts

KW - closure

KW - polyhedrality

UR - http://www.scopus.com/inward/record.url?scp=84875494729&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-36694-9_13

DO - 10.1007/978-3-642-36694-9_13

M3 - Conference contribution

AN - SCOPUS:84875494729

SN - 9783642366932

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 145

EP - 156

BT - Integer Programming and Combinatorial Optimization - 16th International Conference, IPCO 2013, Proceedings

T2 - 16th Conference on Integer Programming and Combinatorial Optimization, IPCO 2013

Y2 - 18 March 2013 through 20 March 2013

ER -