Madsen, K.Nielsen H. B.Pınar, M. Ç.2016-02-082016-02-0819940167-6377http://hdl.handle.net/11693/26012New 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.EnglishCharacterizationHuber functionsNon-smooth optimizationOverdetermined linear systemsSmoothingℓ1 optimizationApproximation theoryFunctionsLinear algebraMathematical operatorsOptimizationVectorsHuber functionsNon-smooth optimizationOverdetermined linear systemsSmoothingOperations researchArticle10.1016/0167-6377(94)90027-21872-7468