Linear programming and \(\ell _ 1\) regression: A geometric interpretation
type: Item
instance of: scholarly article
title: Linear programming and \(\ell _ 1\) regression: A geometric interpretation
zbMATH Open document ID: 0624.62067
DOI: 10.1016/0167-9473(87)90050-8
author: J. J. Brennan
author: Lawrence M. Seiford
published in: Computational Statistics and Data Analysis
publication date: 1987-01-01T00:00:00Z
review text: Approaches to the solution of the \(\ell_ 1\) estimation problem have a long history, going back to at least Edgeworth in the nineteenth century. Modern solution approaches have been of two types: (i) descent methods and (ii) primal or dual LP methods. Simplex based algorithms have a standard geometric interpretation, but occasionally much more tangible geometric insights are available. For example, in the capacitated transhipment problem the workings of the LP solution algorithm can be interpreted on the underlying network. In this paper we develop geometric insight into the solution process directly in the space where the problem originates - the space of observations.
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 90C05
zbMATH DE Number: 4013792
zbMATH Keywords: \(\ell 1\)-regression
zbMATH Keywords: absolute value regression
MaRDI profile type: Publication
full work available at URL: 0167-9473(87)90050-8
OpenAlex ID: W2042373493
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description: scientific article; zbMATH DE number 4013792