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Minimum L1-distance projection onto the boundary of a convex set: Simple characterization

Hans J. H. Tuenter
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Abstract

We show that the minimum distance projection in the L1-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.

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Hans J. H. Tuenter. 2006-06-18. Minimum L1-distance projection onto the boundary of a convex set: Simple characterization. https://doi.org/10.1023/a%3A1013614208950

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