Table of Contents
ISRN Operations Research
Volume 2013, Article ID 230717, 9 pages
http://dx.doi.org/10.1155/2013/230717
Research Article

A Mixed Line Search Smoothing Quasi-Newton Method for Solving Linear Second-Order Cone Programming Problem

1School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China
2School of Electronic Engineering and Automation, Guilin University of Electronic Technology, Guilin 541004, China

Received 30 January 2013; Accepted 19 February 2013

Academic Editors: W. Bein, A. Piunovskiy, and G. Silva

Copyright © 2013 Zhuqing Gui 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. Y. E. Nesterov and M. J. Todd, “Self-scaled barriers and interior-point methods for convex programming,” Mathematics of Operations Research, vol. 22, no. 1, pp. 1–42, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. Y. E. Nesterov and M. J. Todd, “Primal-dual interior-point methods for self-scaled cones,” SIAM Journal on Optimization, vol. 8, no. 2, pp. 324–364, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. X. N. Chi and S. Y. Liu, “A predictor-corrector smoothing method for second-order cone programming,” Journal of Systems Science and Mathematical Sciences, vol. 29, no. 4, pp. 547–554, 2009. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. Y. J. Liu, L. W. Zhang, and Y. H. Wang, “Convergence properties of a smoothing method for linear second-order cone programming,” Advances in Mathematics, vol. 36, no. 4, pp. 491–502, 2007. View at Google Scholar · View at MathSciNet
  5. M. Fukushima, Z.-Q. Luo, and P. Tseng, “Smoothing functions for second-order-cone complementarity problems,” SIAM Journal on Optimization, vol. 12, no. 2, pp. 436–460, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  6. A. Griewank, “The “global” convergence of Broyden-like methods with a suitable line search,” The Journal of the Australian Mathematical Society B, vol. 28, no. 1, pp. 75–92, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. D. H. Li and M. Fukushima, “A derivative-free line search and DFP method for symmetric equations with global and superlinear convergence,” Numerical Functional Analysis and Optimization, vol. 20, no. 1-2, pp. 59–77, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. J. E. Dennis Jr. and J. J. Moré, “A characterization of superlinear convergence and its application to quasi-Newton methods,” Mathematics of Computation, vol. 28, pp. 549–560, 1974. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. D.-H. Li and M. Fukushima, “A derivative-free line search and global convergence of Broyden-like method for nonlinear equations,” Optimization Methods and Software, vol. 13, no. 3, pp. 181–201, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet