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

Author

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  • H. J. H. Tuenter

    (York University)

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).

Suggested Citation

  • H. J. H. Tuenter, 2002. "Minimum L1-Distance Projection onto the Boundary of a Convex Set: Simple Characterization," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 441-445, February.
    • Handle: RePEc:spr:joptap:v:112:y:2002:i:2:d:10.1023_a:1013614208950
    DOI: 10.1023/A:1013614208950
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    Cited by:

    1. Sekitani, Kazuyuki & Zhao, Yu, 2023. "Least-distance approach for efficiency analysis: A framework for nonlinear DEA models," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1296-1310.
    2. Zhu, Qingyuan & Wu, Jie & Ji, Xiang & Li, Feng, 2018. "A simple MILP to determine closest targets in non-oriented DEA model satisfying strong monotonicity," Omega, Elsevier, vol. 79(C), pages 1-8.

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