About this Journal Submit a Manuscript Table of Contents
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

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.

Linked References

  1. J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, NY, USA, 1970. View at MathSciNet
  2. E. Zeidler, Nonlinear functional analysis and its applications. II/B: Nonlinear monotone operators, Springer, New York, NY, USA, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  3. A. N. Iusem and M. V. Solodov, “Newton-type methods with generalized distances for constrained optimization,” Optimization, vol. 41, no. 3, pp. 257–278, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. Y.-B. Zhao and D. Li, “Monotonicity of fixed point and normal mappings associated with variational inequality and its application,” SIAM Journal on Optimization, vol. 11, no. 4, pp. 962–973, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. M. V. Solodov and B. F. Svaiter, “A globally convergent inexact Newton method for systems of monotone equations,” in Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, vol. 22, pp. 355–369, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1999. View at Zentralblatt MATH · View at MathSciNet
  6. L. Zhang and W. Zhou, “Spectral gradient projection method for solving nonlinear monotone equations,” Journal of Computational and Applied Mathematics, vol. 196, no. 2, pp. 478–484, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. Y. Xiao, Q. Wang, and Q. Hu, “Non-smooth equations based method for l1-norm problems with applications to compressed sensing,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 11, pp. 3570–3577, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  8. K. Yin, Y. Xiao, and M. Zhang, “Nonlinear conjugate gradient method for l1-norm regularization problems in compressive sensing,” Journal of Computational Information Systems, vol. 7, no. 3, pp. 880–885, 2011. View at Scopus
  9. G. Yu, “A derivative-free method for solving large-scale nonlinear systems of equations,” Journal of Industrial and Management Optimization, vol. 6, no. 1, pp. 149–160, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. G. Yu, “Nonmonotone spectral gradient-type methods for large-scale unconstrained optimization and nonlinear systems of equations,” Pacific Journal of Optimization, vol. 7, no. 2, pp. 387–404, 2011. View at Zentralblatt MATH · View at MathSciNet
  11. G. Yu, S. Niu, and J. Ma, “Multivariate spectral gradient projection method for nonlinear monotone equations with convex constraints,” Journal of Industrial and Management Optimization, vol. 9, no. 1, pp. 117–129, 2013. View at MathSciNet
  12. L. Han, G. Yu, and L. Guan, “Multivariate spectral gradient method for unconstrained optimization,” Applied Mathematics and Computation, vol. 201, no. 1-2, pp. 621–630, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. E. D. Dolan and J. J. Moré, “Benchmarking optimization software with performance profiles,” Mathematical Programming, vol. 91, no. 2, pp. 201–213, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE Journal on Selected Topics in Signal Processing, vol. 1, no. 4, pp. 586–597, 2007. View at Publisher · View at Google Scholar · View at Scopus