Abstract
Given a point d and a convex polyhedron or polyhedral cone in a real complete inner product space. We shall describe a numerical method to find a point in the polyhedron (cone) which has minimum distance to d. The characteristics of our method are the description of the polyhedron (cone) by its extreme points (rays) and the introduction of a one-parameter family of problems including a trivially solvable problem and the given problem. The knowledge of the solution of the problem corresponding to one value of the parameter makes it easy to find a larger parameter value for which the solution can again be found. Starting with the trivially solvable problem, the given problem is reached in a finite number of steps. Computational experience shows that the computation time is about proportional to the product of the dimension of the space and the number of extreme points in the polyhedron, when these two quantities are of the same order of magnitude.
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The Swedish Natural Science Research Council has partly sponsored the work.
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Philip, J. A quadratic programming algorithm. Z. Wahrscheinlichkeitstheorie verw Gebiete 5, 55–70 (1966). https://doi.org/10.1007/BF00532812
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DOI: https://doi.org/10.1007/BF00532812