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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 780107, 5 pages
A New Smoothing Nonlinear Conjugate Gradient Method for Nonsmooth Equations with Finitely Many Maximum Functions
1College of Mathematics, Qingdao University, Qingdao 266071, China
2School of Management, University of Shanghai for Science and Technology, Shanghai 200093, China
Received 8 March 2013; Accepted 25 March 2013
Academic Editor: Yisheng Song
Copyright © 2013 Yuan-yuan Chen and Shou-qiang Du. 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.
- L. Qi and P. Tseng, “On almost smooth functions and piecewise smooth functions,” Nonlinear Analysis, vol. 67, no. 3, pp. 773–794, 2007.
- F. Facchinei and J.-S. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems, vol. 1, Springer, New York, NY, USA, 2003.
- D. Sun and J. Han, “Newton and quasi-Newton methods for a class of nonsmooth equations and related problems,” SIAM Journal on Optimization, vol. 7, no. 2, pp. 463–480, 1997.
- Y. Gao, “Newton methods for solving two classes of nonsmooth equations,” Applications of Mathematics, vol. 46, no. 3, pp. 215–229, 2001.
- S.-Q. Du and Y. Gao, “A parametrized Newton method for nonsmooth equations with finitely many maximum functions,” Applications of Mathematics, vol. 54, no. 5, pp. 381–390, 2009.
- N. Yamashita and M. Fukushima, “Modified Newton methods for solving a semismooth reformulation of monotone complementarity problems,” Mathematical Programming B, vol. 76, no. 3, pp. 469–491, 1997.
- L. Q. Qi and J. Sun, “A nonsmooth version of Newton's method,” Mathematical Programming A, vol. 58, no. 3, pp. 353–367, 1993.
- Y. Elfoutayeni and M. Khaladi, “Using vector divisions in solving the linear complementarity problem,” Journal of Computational and Applied Mathematics, vol. 236, no. 7, pp. 1919–1925, 2012.
- X. Chen and W. Zhou, “Smoothing nonlinear conjugate gradient method for image restoration using nonsmooth nonconvex minimization,” SIAM Journal on Imaging Sciences, vol. 3, no. 4, pp. 765–790, 2010.
- X. Chen, “Smoothing methods for nonsmooth, nonconvex minimization,” Mathematical Programming B, vol. 134, no. 1, pp. 71–99, 2012.
- M. C. Ferris, O. L. Mangasarian, and J. S. Pang, Complementarity: Applications, Algorithms and Extensions, Kluwer Academic, Dordrecht, The Netherlands, 2001.
- Y. H. Dai and Y. Yuan, “A nonlinear conjugate gradient method with a strong global convergence property,” SIAM Journal on Optimization, vol. 10, no. 1, pp. 177–182, 1999.
- Z. Dai and F. Wen, “Global convergence of a modified Hestenes-Stiefel nonlinear conjugate gradient method with Armijo line search,” Numerical Algorithms, vol. 59, no. 1, pp. 79–93, 2012.
- C.-Y. Wang, Y.-Y. Chen, and S.-Q. Du, “Further insight into the Shamanskii modification of Newton method,” Applied Mathematics and Computation, vol. 180, no. 1, pp. 46–52, 2006.
- Y. Y. Chen and S. Q. Du, “Nonlinear conjugate gradient methods with Wolfe type line search,” Abstract and Applied Analysis, vol. 2013, Article ID 742815, 5 pages, 2013.
- Y. Xiao, H. Song, and Z. Wang, “A modified conjugate gradient algorithm with cyclic Barzilai-Borwein steplength for unconstrained optimization,” Journal of Computational and Applied Mathematics, vol. 236, no. 13, pp. 3101–3110, 2012.
- S. Zhou and Z. Zou, “A relaxation scheme for Hamilton-Jacobi-Bellman equations,” Applied Mathematics and Computation, vol. 186, no. 1, pp. 806–813, 2007.
- X. Chen, L. Qi, and D. Sun, “Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities,” Mathematics of Computation, vol. 67, no. 222, pp. 519–540, 1998.
- M. C. Ferris and J. S. Pang, “Engineering and economic applications of complementarity problems,” SIAM Review, vol. 39, no. 4, pp. 669–713, 1997.