Minimum L1-Distance Projection onto the Boundary of a Convex Set: Simple Characterization |
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Authors: | Tuenter H J H |
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Institution: | (1) Schulich School of Business, York University, Toronto, Ontario, Canada |
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Abstract: | We show that the minimum distance projection in the L
1-norm from an interior point onto the boundary of a convex set is achieved by a single, unidimensional projection. Application of this characterization when the convex set is a polyhedron leads to either an elementary minmax problem or a set of easily solved linear programs, depending upon whether the polyhedron is given as the intersection of a set of half spaces or as the convex hull of a set of extreme points. The outcome is an easier and more straightforward derivation of the special case results given in a recent paper by Briec (Ref. 1). |
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Keywords: | Convex sets minimum distance projection L
1-norm |
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