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Poster

Solving large-scale nonnegative least-squares

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Sra,  S
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Sra, S. (2010). Solving large-scale nonnegative least-squares. Poster presented at 16th Conference of the International Linear Algebra Society (ILAS 2010), Pisa, Italy.


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 Hanson [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 exploiting
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 convex solvers
and specialized NNLS algorithms. The numerical results suggest
that BBSG is a practical method for solving large-scale
NNLS problems.