  


On Maximal Sfree Convex Sets
Diego A. Moran R. (dmoranisye.gatech.edu) Abstract: Let S be a subset of integer points that satisfy the property that $conv(S) \cap Z^n = S$. Then a convex set K is called an Sfree convex set if $int(K) \cap S = \emptyset$. A maximal Sfree convex set is an Sfree convex set that is not properly contained in any Sfree convex set. We show that maximal Sfree convex sets are polyhedra. This result generalizes a result of Basu et al. (2010) for the case where S is the set of integer points in a rational polyhedron and a result of Lovasz (1989) and Basu et al. (2009) for the case where $S$ is the set of integer points in some affine subspace of $R^n$. Keywords: Integer nonlinear programming, Cutting planes, Maximal latticefree convex sets Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming ) Category 2: Integer Programming (Cutting Plane Approaches ) Citation: Download: [PDF] Entry Submitted: 05/29/2010 Modify/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  