2012/04/08 by Yogesh P. Awate, Awate, Yogesh P.
Engineering · #Advanced Surface Polishing Techniques #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Manufacturing Process and Optimization #Optimization and Control (math.OC) #Optimization and Packing Problems
paper · pdf · doi:10.48550/arxiv.1204.1715
openalex publication_date 2012/04/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The corner polyhedron is described by minimal valid inequalities from maximal lattice-free convex sets. For the Relaxed Corner Polyhedron (RCP) with two free integer variables and any number of non-negative continuous variables, it is known that such facet defining inequalities arise from maximal lattice-free splits, triangles and quadrilaterals. We improve on the tightest known upper bound for the approximation of the RCP, purely by minimal valid inequalities from maximal lattice-free quadrilaterals, from 2 to 1.71. We generalize the tightest known lower bound of 1.125 for the approximation of the RCP, purely by minimal valid inequalities from maximal lattice-free triangles, to an infinite subclass of quadrilaterals.