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  Solving Large-Scale Nonnegative Least Squares

Sra, S. (2010). Solving Large-Scale Nonnegative Least Squares. In 16th Conference of the International Linear Algebra Society (ILAS 2010) (pp. 67).

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Sra, S1, 2, Author           
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1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 Abstract: We study the fundamental problem of nonnegative least squares. This problem was apparently introduced by Lawson and Hanson [1] under the name NNLS. As is evident from its name, NNLS seeks least-squares solutions that are also nonnegative. Owing to its wide-applicability numerous algorithms have been derived for NNLS, beginning from the active-set approach of Lawson and Han- son [1] leading up to the sophisticated interior-point method of Bellavia et al. [2]. We present a new algorithm for NNLS that combines projected subgradients with the non-monotonic gradient descent idea of Barzilai and Borwein [3]. Our resulting algorithm is called BBSG, and we guarantee its convergence by ex- ploiting properties of NNLS in conjunction with projected subgradients. BBSG is surprisingly simple and scales well to large problems. We substantiate our claims by empirically evaluating BBSG and comparing it with established con- vex solvers and specialized NNLS algorithms. The numerical results suggest that BBSG is a practical method for solving large-scale NNLS problems.

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 Dates: 2010-06
 Publication Status: Published in print
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 Identifiers: BibTex Citekey: 6839
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Title: 16th Conference of the International Linear Algebra Society (ILAS 2010)
Place of Event: Pisa, Italy
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Title: 16th Conference of the International Linear Algebra Society (ILAS 2010)
Source Genre: Proceedings
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Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 67 Identifier: -