Abstract and Applied Analysis
Volume 2013 (2013), Article ID 619123, 13 pages
http://dx.doi.org/10.1155/2013/619123
Research Article

An Adaptive Prediction-Correction Method for Solving Large-Scale Nonlinear Systems of Monotone Equations with Applications

Gaohang Yu,1 Shanzhou Niu,2 Jianhua Ma,2 and Yisheng Song3

1School of Mathematics and Computer Sciences, Gannan Normal University, Ganzhou 341000, China
2School of Biomedical Engineering, Southern Medical University, Guangzhou 510515, China
3Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong

Received 21 February 2013; Accepted 10 April 2013

Academic Editor: Guoyin Li

Copyright © 2013 Gaohang Yu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.