- 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 376403, 9 pages
A Decomposition Method with Redistributed Subroutine for Constrained Nonconvex Optimization
1School of Sciences, Shenyang University, Shenyang 110044, China
2School of Mathematical, Liaoning Normal University, Dalian 116029, China
3School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
Received 6 September 2012; Revised 8 December 2012; Accepted 13 December 2012
Academic Editor: Jean M. Combes
Copyright © 2013 Yuan Lu 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.
- Y. Lu, L.-P. Pang, F.-F. Guo, and Z.-Q. Xia, “A superlinear space decomposition algorithm for constrained nonsmooth convex program,” Journal of Computational and Applied Mathematics, vol. 234, no. 1, pp. 224–232, 2010.
- C. Lemaréchal, F. Oustry, and C. Sagastizábal, “The -Lagrangian of a convex function,” Transactions of the American Mathematical Society, vol. 352, no. 2, pp. 711–729, 2000.
- R. Mifflin and C. Sagastizábal, “-decomposition derivatives for convex max-functions,” in Ill-Posed Variational Problems and Regularization Techniques, R. Tichatschke and M. A. Théra, Eds., vol. 477 of Lecture Notes in Economics and Mathematical Systems, pp. 167–186, Springer, Berlin, Germany, 1999.
- C. Lemaréchal and C. Sagastizábal, “More than first-order developments of convex functions: primal-dual relations,” Journal of Convex Analysis, vol. 3, no. 2, pp. 255–268, 1996.
- R. Mifflin and C. Sagastizábal, “On -theory for functions with primal-dual gradient structure,” SIAM Journal on Optimization, vol. 11, no. 2, pp. 547–571, 2000.
- R. Mifflin and C. Sagastizábal, “Functions with primal-dual gradient structure and -Hessians,” in Nonlinear Optimization and Related Topics, G. Pillo and F. Giannessi, Eds., vol. 36 of Applied Optimization, pp. 219–233, Kluwer Academic Publishers, 2000.
- R. Mifflin and C. Sagastizábal, “Primal-dual gradient structured functions: second-order results; links to epi-derivatives and partly smooth functions,” SIAM Journal on Optimization, vol. 13, no. 4, pp. 1174–1194, 2003.
- R. Mifflin and C. Sagastizábal, “A -algorithm for convex minimization,” Mathematical Programming B, vol. 104, no. 2-3, pp. 583–608, 2005.
- F. Shan, L.-P. Pang, L.-M. Zhu, and Z.-Q. Xia, “A -decomposed method for solving an MPEC problem,” Applied Mathematics and Mechanics, vol. 29, no. 4, pp. 535–540, 2008.
- Y. Lu, L.-P. Pang, J. Shen, and X.-J. Liang, “A decomposition algorithm for convex nondifferentiable minimization with errors,” Journal of Applied Mathematics, vol. 2012, Article ID 215160, 15 pages, 2012.
- A. Daniilidis, C. Sagastizábal, and M. Solodov, “Identifying structure of nonsmooth convex functions by the bundle technique,” SIAM Journal on Optimization, vol. 20, no. 2, pp. 820–840, 2009.
- W. L. Hare, “A proximal method for identifying active manifolds,” Computational Optimization and Applications, vol. 43, no. 2, pp. 295–306, 2009.
- W. L. Hare, “Functions and sets of smooth substructure: relationships and examples,” Computational Optimization and Applications, vol. 33, no. 2-3, pp. 249–270, 2006.
- R. Mifflin, L. Qi, and D. Sun, “Properties of the Moreau-Yosida regularization of a piecewise convex function,” Mathematical Programming A, vol. 84, no. 2, pp. 269–281, 1999.
- R. T. Rockafellar and R. J.-B. Wets, Variational Analysis, vol. 317 of Fundamental Principles of Mathematical Sciences, Springer, Berlin, Germany, 1998.
- R. Mifflin and C. Sagastizábal, “-smoothness and proximal point results for some nonconvex functions,” Optimization Methods & Software, vol. 19, no. 5, pp. 463–478, 2004.
- S. Lang, Real and Functional Analysis, Springer, New York, NY, USA, 3rd edition, 1993.
- W. Hare and C. Sagastizábal, “Computing proximal points of nonconvex functions,” Mathematical Programming B, vol. 116, no. 1-2, pp. 221–258, 2009.
- W. L. Hare and C. Sagastizábal, “A redistributed proximal bundle method for nonconvex optimization,” SIAM Journal on Optimization, vol. 20, no. 5, pp. 2442–2473, 2010.