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  Tackling Box-Constrained Optimization via a New Projected Quasi-Newton Approach

Kim, D., Sra, S., & Dhillon, I. (2010). Tackling Box-Constrained Optimization via a New Projected Quasi-Newton Approach. SIAM Journal on Scientific Computing, 32(6), 3548-3563. doi:10.1137/08073812X.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-BD2A-F Version Permalink: http://hdl.handle.net/21.11116/0000-0002-68AB-9
Genre: Journal Article

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https://epubs.siam.org/doi/10.1137/08073812X (Publisher version)
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 Creators:
Kim, D, Author
Sra, S1, 2, Author              
Dhillon, IS, Author
Affiliations:
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: Numerous scientific applications across a variety of fields depend on box-constrained convex optimization. Box-constrained problems therefore continue to attract research interest. We address box-constrained (strictly convex) problems by deriving two new quasi-Newton algorithms. Our algorithms are positioned between the projected-gradient [J. B. Rosen, J. SIAM, 8 (1960), pp. 181–217] and projected-Newton [D. P. Bertsekas, SIAM J. Control Optim., 20 (1982), pp. 221–246] methods. We also prove their convergence under a simple Armijo step-size rule. We provide experimental results for two particular box-constrained problems: nonnegative least squares (NNLS), and nonnegative Kullback–Leibler (NNKL) minimization. For both NNLS and NNKL our algorithms perform competitively as compared to well-established methods on medium-sized problems; for larger problems our approach frequently outperforms the competition.

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 Dates: 2010-12
 Publication Status: Published in print
 Pages: -
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 Rev. Type: -
 Identifiers: DOI: 10.1137/08073812X
BibTex Citekey: 6765
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Title: SIAM Journal on Scientific Computing
Source Genre: Journal
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Publ. Info: Philadelphia, PA : SIAM
Pages: - Volume / Issue: 32 (6) Sequence Number: - Start / End Page: 3548 - 3563 Identifier: ISSN: 1064-8275
CoNE: https://pure.mpg.de/cone/journals/resource/954928546248