TY - GEN
T1 - A polynomial-time algorithm to check closedness of simple second order mixed-integer sets
AU - Morán Ramírez, Diego Alejandro
AU - Dey, Santanu S.
PY - 2013
Y1 - 2013
N2 - Let Lm be the Lorentz cone in ℝm. Given A ∈ ℚmxn1, and B ∈ ℚmxn2 and b ∈ ℚm, a simple second order conic mixed-integer set (SOCMIS) is a set of the form {(x, y) ∈ ℤn1 x ℝn2 | Ax + By - b ∈ Lm}. We show that there exists a polynomial-time algorithm to check the closedness of the convex hull of simple SOCMISs. Moreover, in the special case of pure integer problems, we present sufficient conditions, that can be checked in polynomial-time, to verify the closedness of intersection of simple SOCMISs.
AB - Let Lm be the Lorentz cone in ℝm. Given A ∈ ℚmxn1, and B ∈ ℚmxn2 and b ∈ ℚm, a simple second order conic mixed-integer set (SOCMIS) is a set of the form {(x, y) ∈ ℤn1 x ℝn2 | Ax + By - b ∈ Lm}. We show that there exists a polynomial-time algorithm to check the closedness of the convex hull of simple SOCMISs. Moreover, in the special case of pure integer problems, we present sufficient conditions, that can be checked in polynomial-time, to verify the closedness of intersection of simple SOCMISs.
KW - Closedness
KW - Mixed-integer convex programming
KW - Polynomial-time algorithm
UR - http://www.scopus.com/inward/record.url?scp=84875496742&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-36694-9_23
DO - 10.1007/978-3-642-36694-9_23
M3 - Conference contribution
AN - SCOPUS:84875496742
SN - 9783642366932
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 266
EP - 277
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 -