New characterizations of \(\ell_ 1\) solutions to overdetermined systems of linear equations

DOI10.1016/0167-6377(94)90027-2zbMath0815.90124OpenAlexW2086183090MaRDI QIDQ1342287

Hans Bruun Nielsen, Kaj Madsen, Mustafa Çelebi Pinar

Publication date: 13 February 1995

Published in: Operations Research Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-6377(94)90027-2

zbMATH Keywords

smoothingnon-smooth optimizationoverdetermined systems of linear equationsHuber problempolyhedral characterization of the solution set

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Nonlinear programming (90C30) Nonsmooth analysis (49J52) Numerical computation of solutions to systems of equations (65H10) Iterative numerical methods for linear systems (65F10)

Related Items (8)

Sparse solutions to an underdetermined system of linear equations via penalized Huber loss ⋮ Minimizers of sparsity regularized Huber loss function ⋮ A characterization of the optimal set of linear programs based on the augmented lagrangian ⋮ Duality in robust linear regression using Huber's \(M\)-estimator ⋮ A penalty continuation method for the \(\ell_\infty\) solution of overdetermined linear systems ⋮ Necessary and Sufficient Conditions for Noiseless Sparse Recovery via Convex Quadratic Splines ⋮ Approximation in normed linear spaces ⋮ An \(L_{1}\) estimation algorithm with degeneracy and linear constraints.

Cites Work

• Finite algorithms for robust linear regression
• The Mathematical Structure of Huber’s M-Estimator
• A Finite Smoothing Algorithm for Linear $l_1 $ Estimation
• Complementarity Theorems for Linear Programming
• Robust Statistics
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