A recursive algorithm for finding the minimum norm point in a polytope and a pair of closest points in two polytopes
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For a given pair of finite point setsP andQ in some Euclidean space we consider two problems: Problem 1 of finding the minimum Euclidean norm point in the convex hull ofP and Problem 2 of finding a minimum Euclidean distance pair of points in the convex hulls ofP andQ. We propose a finite recursive algorithm for these problems. The algorithm is not based on the simplicial decomposition of convex sets and does not require to solve systems of linear equations.
Key wordsMinimum norm point minimum distance pair of points recursive algorithm convex quadratic program
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