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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 619123, 13 pages
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.
- J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, NY, USA, 1970.
- E. Zeidler, Nonlinear functional analysis and its applications. II/B: Nonlinear monotone operators, Springer, New York, NY, USA, 1990.
- 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.
- 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.
- 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.
- 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.
- Y. Xiao, Q. Wang, and Q. Hu, “Non-smooth equations based method for -norm problems with applications to compressed sensing,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 11, pp. 3570–3577, 2011.
- K. Yin, Y. Xiao, and M. Zhang, “Nonlinear conjugate gradient method for -norm regularization problems in compressive sensing,” Journal of Computational Information Systems, vol. 7, no. 3, pp. 880–885, 2011.
- 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.
- 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.
- 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.
- 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.
- E. D. Dolan and J. J. Moré, “Benchmarking optimization software with performance profiles,” Mathematical Programming, vol. 91, no. 2, pp. 201–213, 2002.
- 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.