New Characterizations of Solutions to Overdetermined Systems of Linear|Equations

Kaj Madsen, Hans Bruun Nielsen, M. C. Pinar

    Research output: Contribution to journalJournal articleResearchpeer-review

    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.
    Original languageEnglish
    JournalOperations Research Letters
    Volume16
    Issue number3
    Pages (from-to)159-166
    ISSN0167-6377
    DOIs
    Publication statusPublished - 1994

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