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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 185249, 16 pages
Metric Subregularity for Subsmooth Generalized Constraint Equations in Banach Spaces
1Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, China
2Basic Flight Training Base, Aviation University of Air Force, Changchun, Jilin 130022, China
3School of Science, Kunming University of Science And Technology, Kunming, Yunnan 650500, China
Received 13 October 2012; Accepted 23 November 2012
Academic Editor: Jian-Wen Peng
Copyright © 2012 He Qinghai 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.
- W. Li and I. Singer, “Global error bounds for convex multifunctions and applications,” Mathematics of Operations Research, vol. 23, no. 2, pp. 443–462, 1998.
- X. Y. Zheng and K. F. Ng, “Perturbation analysis of error bounds for systems of conic linear inequalities in Banach spaces,” SIAM Journal on Optimization, vol. 15, no. 4, pp. 1026–1041, 2005.
- W. Li, “Abadie's constraint qualification, metric regularity, and error bounds for differentiable convex inequalities,” SIAM Journal on Optimization, vol. 7, no. 4, pp. 966–978, 1997.
- B. S. Mordukhovich and Y. Shao, “Nonconvex differential calculus for infinite-dimensional multifunctions,” Set-Valued Analysis, vol. 4, no. 3, pp. 205–236, 1996.
- X. Y. Zheng and K. F. Ng, “Metric subregularity and constraint qualifications for convex generalized equations in Banach spaces,” SIAM Journal on Optimization, vol. 18, no. 2, pp. 437–460, 2007.
- X. Y. Zheng and K. F. Ng, “Calmness for -subsmooth multifunctions in Banach spaces,” SIAM Journal on Optimization, vol. 19, no. 4, pp. 1648–1673, 2008.
- D. Klatte and B. Kummer, Nonsmooth Equations in Optimization, vol. 60, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2002.
- B. S. Mordukhovich, “Complete characterization of openness, metric regularity, and Lipschitzian properties of multifunctions,” Transactions of the American Mathematical Society, vol. 340, no. 1, pp. 1–35, 1993.
- B. S. Mordukhovich, Variational Analysis and Generalized Differentiation. I, II, Springer, Berlin, Germany, 2006.
- R. Henrion, A. Jourani, and J. Outrata, “On the calmness of a class of multifunctions,” SIAM Journal on Optimization, vol. 13, no. 2, pp. 603–618, 2002.
- X. Y. Zheng and K. F. Ng, “Metric regularity and constraint qualifications for convex inequalities on Banach spaces,” SIAM Journal on Optimization, vol. 14, no. 3, pp. 757–772, 2003.
- X. Y. Zheng and K. F. Ng, “Linear regularity for a collection of subsmooth sets in Banach spaces,” SIAM Journal on Optimization, vol. 19, no. 1, pp. 62–76, 2008.
- F. H. Clarke, R. J. Stern, and P. R. Wolenski, “Proximal smoothness and the lower- property,” Journal of Convex Analysis, vol. 2, no. 1-2, pp. 117–144, 1995.
- R. A. Poliquin, R. T. Rockafellar, and L. Thibault, “Local differentiability of distance functions,” Transactions of the American Mathematical Society, vol. 352, no. 11, pp. 5231–5249, 2000.
- D. Aussel, A. Daniilidis, and L. Thibault, “Subsmooth sets: functional characterizations and related concepts,” Transactions of the American Mathematical Society, vol. 357, no. 4, pp. 1275–1301, 2005.
- F. H. Clarke, Optimization and Nonsmooth Analysis, John Wiley & Sons, New York, NY, USA, 1983.
- R. R. Phelps, Convex Functions, Monotone Operators and Differentiability, vol. 1364 of Lecture Notes in Mathematics, Springer, New York, NY, USA, 1989.
- R. T. Rockafellar and R. J.-B. Wets, Variational Analysis, vol. 317, Springer, Berlin, Germany, 1998.
- B. S. Mordukhovich and Y. H. Shao, “Nonsmooth sequential analysis in Asplund spaces,” Transactions of the American Mathematical Society, vol. 348, no. 4, pp. 1235–1280, 1996.