- 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 176363, 8 pages
Strong Duality and Optimality Conditions for Generalized Equilibrium Problems
1College of Mathematics and Statistics, Jishou University, Jishou 416000, China
2Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan
3School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan 316004, China
Received 29 August 2013; Accepted 4 September 2013
Academic Editor: Jen-Chih Yao
Copyright © 2013 D. H. Fang and J. F. Bao. 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.
- C. Zălinescu, Convex Analysis in General Vector Spaces, World Scientific Publishing, River Edge, NJ, USA, 2002.
- M. A. Noor and K. I. Noor, “On equilibrium problems,” Applied Mathematics E-Notes, vol. 4, pp. 125–132, 2004.
- G. Bigi, M. Castellani, and G. Kassay, “A dual view of equilibrium problems,” Journal of Mathematical Analysis and Applications, vol. 342, no. 1, pp. 17–26, 2008.
- E. Blum and W. Oettli, “From optimization and variational inequalities to equilibrium problems,” The Mathematics Student, vol. 63, no. 1–4, pp. 123–145, 1994.
- N. Dinh, J. J. Strodiot, and V. H. Nguyen, “Duality and optimality conditions for generalized equilibrium problems involving DC functions,” Journal of Global Optimization, vol. 48, no. 2, pp. 183–208, 2010.
- D. H. Fang, C. Li, and K. F. Ng, “Constraint qualifications for extended Farkas's lemmas and Lagrangian dualities in convex infinite programming,” SIAM Journal on Optimization, vol. 20, no. 3, pp. 1311–1332, 2009.
- A. N. Iusem and W. Sosa, “Iterative algorithms for equilibrium problems,” Optimization, vol. 52, no. 3, pp. 301–316, 2003.
- L. D. Muu, V. H. Nguyen, and N. V. Quy, “On Nash-Cournot oligopolistic market equilibrium models with concave cost functions,” Journal of Global Optimization, vol. 41, no. 3, pp. 351–364, 2008.
- L. D. Muu and W. Oettli, “Convergence of an adaptive penalty scheme for finding constrained equilibria,” Nonlinear Analysis. Theory, Methods & Applications, vol. 18, no. 12, pp. 1159–1166, 1992.
- T. T. V. Nguyen, J. J. Strodiot, and V. H. Nguyen, “A bundle method for solving equilibrium problems,” Mathematical Programming, vol. 116, no. 1-2, pp. 529–552, 2009.
- I. V. Konnov and S. Schaible, “Duality for equilibrium problems under generalized monotonicity,” Journal of Optimization Theory and Applications, vol. 104, no. 2, pp. 395–408, 2000.
- J. E. Martínez-Legaz and W. Sosa, “Duality for equilibrium problems,” Journal of Global Optimization, vol. 35, no. 2, pp. 311–319, 2006.
- F. M. O. Jacinto and S. Scheimberg, “Duality for generalized equilibrium problem,” Optimization, vol. 57, no. 6, pp. 795–805, 2008.
- L. Altangerel, R. I. Boţ, and G. Wanka, “On the construction of gap functions for variational inequalities via conjugate duality,” Asia-Pacific Journal of Operational Research, vol. 24, no. 3, pp. 353–371, 2007.
- L. Altangerel, R. I. Boţ, and G. Wanka, “On gap functions for equilibrium problems via Fenchel duality,” Pacific Journal of Optimization, vol. 2, no. 3, pp. 667–678, 2006.
- U. Mosco, “Dual variational inequalities,” Journal of Mathematical Analysis and Applications, vol. 40, pp. 202–206, 1972.
- D. H. Fang, C. Li, and X. Q. Yang, “Stable and total Fenchel duality for DC optimization problems in locally convex spaces,” SIAM Journal on Optimization, vol. 21, no. 3, pp. 730–760, 2011.
- B. S. Mordukhovich, N. M. Nam, and N. D. Yen, “Fréchet subdifferential calculus and optimality conditions in nondifferentiable programming,” Optimization, vol. 55, no. 5-6, pp. 685–708, 2006.
- B. S. Mordukhovich, Variational Analysis and Generalized Differentiation, vol. 330, Springer, Berlin, Germany, 2006.