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

  • Authors:

  • H. J. H. Tuenter

  • Affiliations:

  • Postdoctoral Fellow, Schulich School of Business, York University, Toronto, Ontario, Canada

  • Venue:
  • Journal of Optimization Theory and Applications
  • Year:
  • 2002

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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 (Ref. 1).