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Advances in Operations Research
Volume 2012 (2012), Article ID 281396, 20 pages
http://dx.doi.org/10.1155/2012/281396
Research Article

An Asymmetric Proximal Decomposition Method for Convex Programming with Linearly Coupling Constraints

1Institute of System Engineering, Southeast University, Nanjing 210096, China
2Department of Mathematics, Nanjing University, Nanjing 210093, China
3Department of Mathematics, Guangxi Normal University, Guilin 541004, China

Received 17 November 2011; Accepted 10 January 2012

Academic Editor: Abdellah Bnouhachem

Copyright © 2012 Xiaoling Fu 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. R. T. Rockafellar and R. J.-B. Wets, “Generalized linear-quadratic problems of deterministic and stochastic optimal control in discrete time,” SIAM Journal on Control and Optimization, vol. 28, no. 4, pp. 810–822, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. B. Martinet, “Régularisation d'inéquations variationnelles par approximations successives,” Revue Francaise d'Informatique et de Recherche Opérationelle, vol. 4, pp. 154–158, 1970. View at Google Scholar · View at Zentralblatt MATH
  3. R. T. Rockafellar, “Monotone operators and the proximal point algorithm,” SIAM Journal on Control and Optimization, vol. 14, no. 5, pp. 877–898, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. R. T. Rockafellar, “Augmented Lagrangians and applications of the proximal point algorithm in convex programming,” Mathematics of Operations Research, vol. 1, no. 2, pp. 97–116, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. A. Auslender, M. Teboulle, and S. Ben-Tiba, “A logarithmic-quadratic proximal method for variational inequalities,” Computational Optimization and Applications, vol. 12, no. 1-3, pp. 31–40, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. Y. Censor and S. A. Zenios, “Proximal minimization algorithm with D-functions,” Journal of Optimization Theory and Applications, vol. 73, no. 3, pp. 451–464, 1992. View at Publisher · View at Google Scholar
  7. B. He, X. Yuan, and J. J. Z. Zhang, “Comparison of two kinds of prediction-correction methods for monotone variational inequalities,” Computational Optimization and Applications, vol. 27, no. 3, pp. 247–267, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. A. Nemirovsky, Prox-method with rate of convergence 0(1/k) for smooth variational inequalities and saddle point problem, Draft of 30/10/2003.
  9. M. Teboulle, “Convergence of proximal-like algorithms,” SIAM Journal on Optimization, vol. 7, no. 4, pp. 1069–1083, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. D. P. Bertsekas and J. N. Tsitsiklis, Parallel and Distributed Computation, Numerical Methods, Prentice Hall, Englewood Cliffs, NJ, USA, 1989.
  11. G. Chen and M. Teboulle, “A proximal-based decomposition method for convex minimization problems,” Mathematical Programming, vol. 64, no. 1, Ser. A, pp. 81–101, 1994. View at Publisher · View at Google Scholar
  12. B. He, L.-Z. Liao, and S. Wang, “Self-adaptive operator splitting methods for monotone variational inequalities,” Numerische Mathematik, vol. 94, no. 4, pp. 715–737, 2003. View at Google Scholar · View at Zentralblatt MATH
  13. P. Mahey, S. Oualibouch, and D. T. Pham, “Proximal decomposition on the graph of a maximal monotone operator,” SIAM Journal on Optimization, vol. 5, no. 2, pp. 454–466, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. P. Tseng, “Applications of a splitting algorithm to decomposition in convex programming and variational inequalities,” SIAM Journal on Control and Optimization, vol. 29, no. 1, pp. 119–138, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. R. Glowinski and P. Le Tallec, Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics, vol. 9 of SIAM Studies in Applied Mathematics, SIAM, Philadelphia, Pa, USA, 1989.
  16. B.-S. He, H. Yang, and C.-S. Zhang, “A modified augmented Lagrangian method for a class of monotone variational inequalities,” European Journal of Operational Research, vol. 159, no. 1, pp. 35–51, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. M. Fukushima, “Application of the alternating direction method of multipliers to separable convex programming problems,” Computational Optimization and Applications, vol. 1, no. 1, pp. 93–111, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. J. Nocedal and S. J. Wright, Numerical Optimization, Springer Series in Operations Research, Springer, New York, NY, USA, 1999. View at Publisher · View at Google Scholar
  19. A. Hamdi and P. Mahey, “Separable diagonalized multiplier method for decomposing nonlinear programs,” Computational & Applied Mathematics, vol. 19, no. 1, p. 1–29, 125, 2000. View at Google Scholar
  20. A. Hamdi, P. Mahey, and J. P. Dussault, “A new decomposition method in nonconvex programming via a separable augmented Lagrangian,” in Recent advances in Optimization, vol. 452 of Lecture Notes in Economics and Mathematical Systems, pp. 90–104, Springer, Berlin, Germany, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. 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 Zentralblatt MATH
  22. B. S. He, X. L. Fu, and Z. K. Jiang, “Proximal-point algorithm using a linear proximal term,” Journal of Optimization Theory and Applications, vol. 141, no. 2, pp. 299–319, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. E. H. Zarantonello, “Projections on convex sets in Hilbert space and spectral theory,” in Contributions to Nonlinear Functional Analysis, E. H. Zarantonello, Ed., Academic Press, New York, NY, USA, 1971. View at Google Scholar · View at Zentralblatt MATH