Sparse solutions to an underdetermined system of linear equations via penalized Huber loss

Date

2020

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Source Title

Optimization and Engineering

Print ISSN

1389-4420

Electronic ISSN

1573-2924

Publisher

Springer

Volume

Issue

22

Pages

1521 - 1537

Language

English

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Abstract

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.

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Published Version (Please cite this version)