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

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons76142

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

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Zitation

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.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-0013-BD2A-F
Zusammenfassung
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.