New characterizations of ℓ1 solutions to overdetermined systems of linear equations

Date
1994
Authors
Madsen, K.
Nielsen H. B.
Pınar, M. Ç.
Advisor
Supervisor
Co-Advisor
Co-Supervisor
Instructor
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
Journal Title
Journal ISSN
Volume Title
Series
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.

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Book Title
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
Citation
Published Version (Please cite this version)