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

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

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Article ID: iaor20119937
Volume: 50
Issue: 2
Start Page Number: 351
End Page Number: 378
Publication Date: Oct 2011
Journal: Computational Optimization and Applications
Authors: , ,
Keywords: optimization
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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