Approximate Vertex Enumeration
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The problem to compute a V-polytope which is close to a given H-polytope is addressed. Both polytopes are not required to be combinatorially equivalent. This raises the question whether approximate vertex enumeration is easier to realize than exact vertex enumeration. Beyond direct potential applications, approximate vertex enumeration could serve as a model to understand numerical problems with floating point implementations of exact methods. An approximate variant of Motzkin's double description method is developed. Under certain conditions we are able to control the approximation error and to prove correctness of the algorithm for arbitrary polytopes. For dimension 2 and 3 these conditions can be omitted, which allows an easy implementation of the method. It remains open if the conditions are required for dimension larger than 3.
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