Computational Optimization and Applications

, Volume 50, Issue 2, pp 351–378 | Cite as

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

  • Chen Ling
  • Hongxia Yin
  • Guanglu Zhou


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.


L2 spectral estimation Smoothing Newton-type method Semismoothness Superlinear convergence 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.School of ScienceHangzhou Dianzi UniversityHangzhouChina
  2. 2.Department of Mathematics and StatisticsMinnesota State University MankatoMankatoUSA
  3. 3.Department of Mathematics and StatisticsCurtin University of TechnologyPerthAustralia

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