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      New characterizations of ℓ1 solutions to overdetermined systems of linear equations

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      Author(s)
      Madsen, K.
      Nielsen H. B.
      Pınar, M. Ç.
      Date
      1994
      Source Title
      Operations Research Letters
      Print ISSN
      0167-6377
      Electronic ISSN
      1872-7468
      Publisher
      Elsevier
      Volume
      16
      Issue
      3
      Pages
      159 - 166
      Language
      English
      Type
      Article
      Item Usage Stats
      207
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      Abstract
      New characterizations of the ℓ1 solutions to overdetermined system of linear equations are given. The first is a polyhedral characterization of the solution set in terms of a special sign vector using a simple property of the ℓ1 solutions. The second characterization is based on a smooth approximation of the ℓ1 function using a "Huber" function. This allows a description of the solution set of the ℓ1 problem from any solution to the approximating problem for sufficiently small positive values of an approximation parameter. A sign approximation property of the Huber problem is also considered and a characterization of this property is given. © 1994.
      Keywords
      Characterization
      Huber functions
      Non-smooth optimization
      Overdetermined linear systems
      Smoothing
      ℓ1 optimization
      Approximation theory
      Functions
      Linear algebra
      Mathematical operators
      Optimization
      Vectors
      Huber functions
      Non-smooth optimization
      Overdetermined linear systems
      Smoothing
      Operations research
      Permalink
      http://hdl.handle.net/11693/26012
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/0167-6377(94)90027-2
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      • Department of Industrial Engineering 758
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