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2013 An Adaptive Prediction-Correction Method for Solving Large-Scale Nonlinear Systems of Monotone Equations with Applications
Gaohang Yu, Shanzhou Niu, Jianhua Ma, Yisheng Song
Abstr. Appl. Anal. 2013(SI01): 1-13 (2013). DOI: 10.1155/2013/619123

Abstract

Combining multivariate spectral gradient method with projection scheme, this paper presents an adaptive prediction-correction method for solving large-scale nonlinear systems of monotone equations. The proposed method possesses some favorable properties: (1) it is progressive step by step, that is, the distance between iterates and the solution set is decreasing monotonically; (2) global convergence result is independent of the merit function and its Lipschitz continuity; (3) it is a derivative-free method and could be applied for solving large-scale nonsmooth equations due to its lower storage requirement. Preliminary numerical results show that the proposed method is very effective. Some practical applications of the proposed method are demonstrated and tested on sparse signal reconstruction, compressed sensing, and image deconvolution problems.

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Gaohang Yu. Shanzhou Niu. Jianhua Ma. Yisheng Song. "An Adaptive Prediction-Correction Method for Solving Large-Scale Nonlinear Systems of Monotone Equations with Applications." Abstr. Appl. Anal. 2013 (SI01) 1 - 13, 2013. https://doi.org/10.1155/2013/619123

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1275.65029
MathSciNet: MR3055929
Digital Object Identifier: 10.1155/2013/619123

Rights: Copyright © 2013 Hindawi

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Vol.2013 • No. SI01 • 2013
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