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    New characterizations of ℓ1 solutions to overdetermined systems of linear equations
    (Elsevier, 1994) Madsen, K.; Nielsen H. B.; Pınar, M. Ç.
    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.