- Closedness of Integer Hulls of Simple Conic Sets Diego Moran (dmorangatech.edu) Santanu S. Dey (santanu.deyisye.gatech.edu) Abstract: Let $C$ be a full-dimensional pointed closed convex cone in $R^m$ obtained by taking the conic hull of a strictly convex set. Given $A \in Q^{m \times n_1}$, $B \in Q^{m \times n_2}$ and $b \in Q^m$, a simple conic mixed-integer set (SCMIS) is a set of the form $\{(x,y)\in Z^{n_1} \times R^{n_2}\,|\,\ Ax +By -b \in C\}$. In this paper, we give a complete characterization of the closedness of convex hulls of SCMISs. Under certain technical conditions on the cone $C$, we show that the closedness characterization can be used to construct a polynomial-time algorithm to check the closedness of convex hulls of SCMISs. Moreover, we also show that the Lorentz cone satisfies these technical conditions. 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 SCMISs. Keywords: Closedness, Polynomial-time algorithm, Mixed-integer convex programming Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming ) Citation: Download: [PDF]Entry Submitted: 06/07/2013Entry Accepted: 06/07/2013Entry Last Modified: 06/07/2013Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.