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Diego Moran (dmorangatech.edu) Abstract: Let $C$ be a fulldimensional 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 mixedinteger 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 polynomialtime 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 polynomialtime, to verify the closedness of intersection of SCMISs. Keywords: Closedness, Polynomialtime algorithm, Mixedinteger convex programming Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming ) Citation: Download: [PDF] Entry Submitted: 06/07/2013 Modify/Update this entry  
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