Linear best approximation using a class of polyhedral norms

DOI10.1007/BF02139472zbMath0755.65011OpenAlexW2017740898MaRDI QIDQ1200539

G. Alistair Watson

Publication date: 16 January 1993

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02139472

zbMATH Keywords

algorithmdescent methodpolyhedral normsNumerical resultslinear best approximation problem

Mathematics Subject Classification ID

Related Items (10)

Variational analysis of the Ky Fan \(k\)-norm ⋮ Linear best approximation using a class of \(k\)-major \(l_ p\) norms ⋮ Deforming $||.||_{1}$ into $||.||_{\infty}$ via Polyhedral Norms: A Pedestrian Approach ⋮ Sparse optimization via vector \(k\)-norm and DC programming with an application to feature selection for support vector machines ⋮ Weakly invariant norms: geometry of spheres in the space of skew-Hermitian matrices ⋮ Polytopal balls arising in optimization ⋮ DC formulations and algorithms for sparse optimization problems ⋮ Feature selection in SVM via polyhedral \(k\)-norm ⋮ Solving nonnegative sparsity-constrained optimization via DC quadratic-piecewise-linear approximations ⋮ On matrix approximation problems with Ky Fan \(k\) norms

Cites Work

• Discrete, linear approximation problems in polyhedral norms
• Minimization Techniques for Piecewise Differentiable Functions: The $l_1$ Solution to an Overdetermined Linear System
• On Cline’s Direct Method for Solving Overdetermined Linear Systems in the $L_\infty $ Sense
• Convex Analysis
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