Solving Large-Scale Nonnegative Least Squares

Sra, S

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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. In 16th Conference of the International Linear Algebra Society (ILAS 2010) (pp. 67).

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-C004-E

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.