Browsing by Subject "Sparse solution"

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    Sparse solutions to an underdetermined system of linear equations via penalized Huber loss
    (Springer, 2020) Kızılkale, C.; Pınar, Mustafa Çelebi
    We investigate the computation of a sparse solution to an underdetermined system of linear equations using the Huber loss function as a proxy for the 1-norm and a quadratic error term à la Lasso. The approach is termed “penalized Huber loss”. The results of the paper allow to calculate a sparse solution using a simple extrapolation formula under a sign constancy condition that can be removed if one works with extreme points. Conditions leading to sign constancy, as well as necessary and sufficient conditions for computation of a sparse solution by penalized Huber loss, and ties among different solutions are presented.