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

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

2006-06-18

arxiv.org/abs/math/0606426v1

Journal of Optimization Theory and Applications, 112(2):441-445, February 2002

Mathematics

Optimization and Control

5 pages

Scientific paper

10.1023/A:1013614208950

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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