A smoothing Newton-type method for solving the L2 spectral estimation problem with lower and upper bounds

Authors:
Chen Ling;Hongxia Yin;Guanglu Zhou
Affiliations:
School of Science, Hangzhou Dianzi University, Hangzhou, China 310018;Department of Mathematics and Statistics, Minnesota State University Mankato, Mankato, USA MN 56001;Department of Mathematics and Statistics, Curtin University of Technology, Perth, Australia 6845
Venue:
Computational Optimization and Applications
Year:
2011

Citing 17
Cited 0

A simple constraint qualification in infinite dimensional programming

Mathematical Programming: Series A and B
A dual approach to multidimensional Lp spectral estimation problems

SIAM Journal on Control and Optimization
Duality relationships for entropy-like minimization problems

SIAM Journal on Control and Optimization
A nonsmooth version of Newton's method

Mathematical Programming: Series A and B
Convergence analysis of some algorithms for solving nonsmooth equations

Mathematics of Operations Research
Lp-spectral estimation with an L∞ -upper bound

Journal of Optimization Theory and Applications
Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities

Mathematics of Computation
Semismooth Karush-Kuhn-Tucker equations and convergence analysis of Newton and quasi-Newton methods for solving these equations

Mathematics of Operations Research
A smoothing Newton method for general nonlinear complementarity problems

Computational Optimization and Applications - Special issue on nonsmooth and smoothing methods
Smoothing Methods and Semismooth Methods for Nondifferentiable Operator Equations

SIAM Journal on Numerical Analysis
A Newton Method for Shape-Preserving Spline Interpolation

SIAM Journal on Optimization
Smoothing functions and smoothing Newton method for complementarity and variational inequality problems

Journal of Optimization Theory and Applications
Differentiability and semismoothness properties of integral functions and their applications

Mathematical Programming: Series A and B
Convergence rate of Newton's method for L2 spectral estimation

Mathematical Programming: Series A and B
A smoothing projected Newton-type algorithm for semi-infinite programming

Computational Optimization and Applications
Maximum entropy and maximum likelihood in spectral estimation

IEEE Transactions on Information Theory
A further result on an implicit function theorem for locally Lipschitz functions

Operations Research Letters

Quantified Score

Hi-index	0.00

Visualization

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.