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• Newton Methods

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• Tackling Box-Constrained Optimization Via a New Projected Quasi-Newton Approach (pdf, software)
  D. Kim, S. Sra, I. Dhillon.
  SIAM Journal on Scientific Computing 30(6), pp. 3548-3563, December 2010.
  
  Bibtex:
  
  @article{kim2010tacklingb, author = "Dongmin Kim AND Suvrit Sra AND Inderjit S. Dhillon", title = "Tackling Box-Constrained Optimization Via a New Projected Quasi-Newton Approach", journal = "SIAM Journal on Scientific Computing", page = "3548–3563", volume = "30", issue = "6", year = "2010", month = "dec", abstract = "Numerous scienti c applications across a variety of elds 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(1), 1960, pp. 181{217], and projected-Newton [D. P. Bertsekas, SIAM J. Cont. & Opt., 20(2), 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 against well-established methods on medium-sized problems; for larger problems our approach frequently outperforms the competition." }