cdd
The program cdd+ (cdd, respectively) is a C++ (ANSI C) implementation of the Double Description Method [MRTT53] for generating all vertices (i.e. extreme points) and extreme rays of a general convex polyhedron given by a system of linear inequalities: P = {x c R^d : Ax <= b } where is an real matrix and is a real dimensional vector. See, [FP96] for an efficient implementation of the double description method which is employed in cdd+. One useful feature of cdd/cdd+ is its capability of handling the dual (reverse) problem without any transformation of data. The dual problem is known to be the (convex) hull problem which is to obtain a linear inequality representation of a convex polyhedron given as the Minkowski sum of the convex hull of a finite set of points and the nonnegative hull of a finite set of points in : , where the Minkowski sum of two subsets and of is defined as . As we see in this manual, the computation can be done in straightforward manner. There is one assumption for the input for hull computation: the polyhedron must be full-dimensional. Besides these basic functions, cdd/cdd+ can solve the general linear programming (LP) problem to maximize (or minimize) a linear function over polyhedron . It is useful mainly for solving dense LP’s with large (say, up to few hundred thousands) and small (say, up to 100).
This software is also referenced in ORMS.
This software is also referenced in ORMS.
Keywords for this software
References in zbMATH (referenced in 85 articles )
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