Abstract
We propose an efficient algorithm for finding the minimum-norm point in the intersection of a polyhedron and a hyperplane, where the polyhedron is expressed as the sum of the convex hull of a finite point set and the conical hull of a finite direction vector set. Our algorithm solves the minimum-norm point problem by directly treating the given original data, the points, the direction vectors and the hyperplane, without computing points and direction vectors which generate the intersection of the polyhedron and the hyperplane. We also show that our algorithm is practically efficient by computational experiments.
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Fujishige, S., Sato, H. & Zhan, P. An algorithm for finding the minimum-norm point in the intersection of a convex polyhedron and a hyperplane. Japan J. Indust. Appl. Math. 11, 245–264 (1994). https://doi.org/10.1007/BF03167224
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DOI: https://doi.org/10.1007/BF03167224