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A smoothing Newton-type method for solving the L 2 spectral estimation problem with lower and upper bounds

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Abstract

This paper discusses the L 2 spectral estimation problem with lower and upper bounds. To the best of our knowledge, it is unknown if the existing methods for this problem have superlinear convergence property or not. In this paper we propose a nonsmooth equation reformulation for this problem. Then we present a smoothing Newton-type method for solving the resulting system of nonsmooth equations. Global and local superlinear convergence of the proposed method are proved under some mild conditions. Numerical tests show that this method is promising.

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Authors and Affiliations

  1. School of Science, Hangzhou Dianzi University, Hangzhou, 310018, China

    Chen Ling

  2. Department of Mathematics and Statistics, Minnesota State University Mankato, 273 Wissink Hall, Mankato, MN 56001, USA

    Hongxia Yin

  3. Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA, 6845, Australia

    Guanglu Zhou

Authors
  1. Chen Ling
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  2. Hongxia Yin
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  3. Guanglu Zhou
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Corresponding author

Correspondence to Chen Ling.

Additional information

Dedicated to Professor Liqun Qi on the occasion of his 65th birthday.

C. Ling’s work was supported by Chinese NSF Grants 10871168 and 10971187. C. Ling’s work was also supported by the Zhenjiang Provincial National Science Foundation of China (Grant No. Y6100366).

H. Yin’s research was supported by FRG of Minnesota State University Mankato and Chinese NSF Grants 10671203, 70531040, and 70621001.

G. Zhou’s work was supported by the Australian Research Council.

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Ling, C., Yin, H. & Zhou, G. A smoothing Newton-type method for solving the L 2 spectral estimation problem with lower and upper bounds. Comput Optim Appl 50, 351–378 (2011). https://doi.org/10.1007/s10589-010-9356-0

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