Minimum L1-Distance Projection onto the Boundary of a Convex Set: Simple Characterization

H. J. H. Tuenter
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H. J. H. Tuenter: York University

Journal of Optimization Theory and Applications, 2002, vol. 112, issue 2, No 9, 445 pages

Abstract: 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).

Keywords: Convex sets; minimum distance projection; L 1-norm (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1023/A:1013614208950

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