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

Y2 - 18 March 2013 through 20 March 2013

ER -