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Interior-Point Gradient Method for Large-Scale Totally Nonnegative Least Squares Problems

Author

Listed:
  • M. Merritt

    (Rice University)

  • Y. Zhang

    (Rice University)

Abstract

We study an interior-point gradient method for solving a class of so-called totally nonnegative least-squares problems. At each iteration, the method decreases the residual norm along a diagonally-scaled negative gradient direction with a special scaling. We establish the global convergence of the method and present some numerical examples to compare the proposed method with a few similar methods including the affine scaling method.

Suggested Citation

  • M. Merritt & Y. Zhang, 2005. "Interior-Point Gradient Method for Large-Scale Totally Nonnegative Least Squares Problems," Journal of Optimization Theory and Applications, Springer, vol. 126(1), pages 191-202, July.
    • Handle: RePEc:spr:joptap:v:126:y:2005:i:1:d:10.1007_s10957-005-2668-z
    DOI: 10.1007/s10957-005-2668-z
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    Cited by:

    1. Jingu Kim & Yunlong He & Haesun Park, 2014. "Algorithms for nonnegative matrix and tensor factorizations: a unified view based on block coordinate descent framework," Journal of Global Optimization, Springer, vol. 58(2), pages 285-319, February.
    2. Andrej Čopar & Blaž Zupan & Marinka Zitnik, 2019. "Fast optimization of non-negative matrix tri-factorization," PLOS ONE, Public Library of Science, vol. 14(6), pages 1-15, June.
    3. Renato D. C. Monteiro & Camilo Ortiz & Benar F. Svaiter, 2016. "An adaptive accelerated first-order method for convex optimization," Computational Optimization and Applications, Springer, vol. 64(1), pages 31-73, May.

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