Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 379734, 10 pages
http://dx.doi.org/10.1155/2015/379734
Research Article

An Alternating Direction Method for Convex Quadratic Second-Order Cone Programming with Bounded Constraints

1School of Mathematics and Statistics, Xidian University, Xi’an 710071, China
2School of Computer Science, Xi’an Science and Technology University, Xi’an 710054, China

Received 20 October 2014; Revised 26 March 2015; Accepted 30 March 2015

Academic Editor: Gerhard-Wilhelm Weber

Copyright © 2015 Xuewen Mu and Yaling Zhang. 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. X. Zhang, Z. Liu, and S. Liu, “A trust region SQP-filter method for nonlinear second-order cone programming,” Computers & Mathematics with Applications, vol. 63, no. 12, pp. 1569–1576, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. H. Kato and M. Fukushima, “An SQP-type algorithm for nonlinear second-order cone programs,” Optimization Letters, vol. 1, no. 2, pp. 129–144, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. X. Y. Zhao, A semismooth Newton-CG augmented Lagrangian method for large scale linear and convex quadratic SDPs [Ph.D. thesis], National University of Singapore, 2009.
  4. J. F. Sturm, “Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones,” Optimization Methods and Software, vol. 11, no. 1–4, pp. 625–653, 1999. View at Publisher · View at Google Scholar
  5. R. H. Tütüncü, K. C. Toh, and M. J. Todd, “Solving semidefinite-quadratic-linear programs using SDPT3,” Mathematical Programming, vol. 95, pp. 189–217, 2003. View at Google Scholar
  6. S. H. Schmieta and F. Alizadeh, “Associative and Jordan algebras, and polynomial time interior-point algorithms for symmetric cones,” Mathematics of Operations Research, vol. 26, no. 3, pp. 543–564, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  7. S. H. Schmieta and F. Alizadeh, “Extension of primal-dual interior point algorithms to symmetric cones,” Mathematical Programming, vol. 96, no. 3, pp. 409–438, 2003. View at Publisher · View at Google Scholar
  8. R. D. Monteiro and T. Tsuchiya, “Polynomial convergence of primal-dual algorithms for the second-order cone program based on the MZ-family of directions,” Mathematical Programming, vol. 88, no. 1, pp. 61–83, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  9. J. Eckstein and D. P. Bertsekas, An Alternating Direction Method for Linear Programming, LIDS-P, Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, Mass, USA, 1967.
  10. Z. Yu, “Solving semidefinite programming problems via alternating direction methods,” Journal of Computational and Applied Mathematics, vol. 193, no. 2, pp. 437–445, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. J. Malick, J. Povh, F. Rendl, and A. Wiegele, “Regularization methods for semidefinite programming,” SIAM Journal on Optimization, vol. 20, no. 1, pp. 336–356, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  12. P. Tseng, “Alternating projection-proximal methods for convex programming and variational inequalities,” SIAM Journal on Optimization, vol. 7, no. 4, pp. 951–965, 1997. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. Y. Wang, J. Yang, W. Yin, and Y. Zhang, “A new alternating minimization algorithm for total variation image reconstruction,” SIAM Journal on Imaging Sciences, vol. 1, no. 3, pp. 248–272, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. J. Yang, Y. Zhang, and W. Yin, “An efficient TVL1 algorithm for deblurring multichannel images corrupted by impulsive noise,” SIAM Journal on Scientific Computing, vol. 31, no. 4, pp. 2842–2865, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  15. J. Sun and S. Zhang, “A modified alternating direction method for convex quadratically constrained quadratic semidefinite programs,” European Journal of Operational Research, vol. 207, no. 3, pp. 1210–1220, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. Z. Wen, D. Goldfarb, and W. Yin, “Alternating direction augmented Lagrangian methods for semidefinite programming,” Mathematical Programming Computation, vol. 2, no. 3-4, pp. 203–230, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  17. U. Faraut and A. Koranyi, Analysis on Symmetric Cone, Oxford University Press, New York, NY, USA, 1994.
  18. J. V. Outrata and D. Sun, “On the coderivative of the projection operator onto the second-order cone,” Set-Valued Analysis, vol. 16, no. 7-8, pp. 999–1014, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. L. C. Kong, L. Tuncel, and N. H. Xiu, “Clarke generalized jacobian of the projection onto symmetric cones,” Set-Valued and Variational Analysis, vol. 17, pp. 135–151, 2009. View at Google Scholar
  20. D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and their Applications, Academic Press, New York, NY, USA, 1980. View at MathSciNet