- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 680768, 8 pages
Convergence Analysis of Alternating Direction Method of Multipliers for a Class of Separable Convex Programming
1School of Mathematical Science and Key Laboratory for NSLSCS of Jiangsu Province, Nanjing Normal University, Nanjing, Jiangsu 210023, China
2College of Mathematics and Information, China West Normal University, Nanchong, Sichuan 637009, China
Received 19 July 2013; Accepted 30 July 2013
Academic Editor: Xu Minghua
Copyright © 2013 Zehui Jia 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.
- D. Gabay and B. Mercier, “A dual algorithm for the solution of nonlinear variational problems via finite element approximation,” Computers and Mathematics with Applications, vol. 2, no. 1, pp. 17–40, 1976.
- D. Gabay, “Applications of the method of multipliers to variational inequalities,” in Augmented Lagrangian Methods: Applications to Numerical Solution of Boundary-Value Problems, M. Fortin and R. Glowinski, Eds., pp. 299–331, North-Holland Publisher, Amsterdam, The Netherland, 1983.
- M. Tao and X. Yuan, “Recovering low-rank and sparse components of matrices from incomplete and noisy observations,” SIAM Journal on Optimization, vol. 21, no. 1, pp. 57–81, 2011.
- M. K. Ng, P. Weiss, and X. Yuan, “Solving constrained total-variation image restoration and reconstruction problems via alternating direction methods,” SIAM Journal on Scientific Computing, vol. 32, no. 5, pp. 2710–2736, 2010.
- L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D, vol. 60, no. 1–4, pp. 259–268, 1992.
- 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.
- D. Han and X. Yuan, “A note on the alternating direction method of multipliers,” Journal of Optimization Theory and Applications, vol. 155, pp. 227–238, 2012.
- D. R. Han, X. M. Yuan, W. X. Zhang, and X. J. Cai, “An ADM-based splitting method for separable convex programming,” Computational Optimization and Applications, vol. 54, pp. 343–369, 2013.
- B. S. He, M. Tao, and X. M. Yuan, “Alternating direction method with Gaussian back substitution for separable convex programming,” SIAM Journal on Optimization, vol. 22, pp. 313–340, 2012.
- B. S. He, M. Tao, M. H. Xu, and X. M. Yuan, “Alternating directions based contraction method for generally separable linearly constrained convex programming problems,” Optimization, vol. 62, pp. 573–596, 2013.
- B. S. He, M. Tao, and X. M. Yuan, “A splitting method for separable convex programming,” IMA Journal of Numerical Analysis. In press.
- D. Han and H. K. Lo, “Solving non-additive traffic assignment problems: a descent method for co-coercive variational inequalities,” European Journal of Operational Research, vol. 159, no. 3, pp. 529–544, 2012.
- F. Facchinei and J. S. Pang, Finite-Dimensional Variational Inequalities and Complementary Problems. Volume I and II, Springer, New York, NY, USA, 2003.