- 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 492103, 4 pages
A Note on Scalar-Valued Gap Functions for Generalized Vector Variational Inequalities
1College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China
2College of Automation, Chongqing University, Chongqing 400030, China
3School of Management, Southwest University of Political Science and Law, Chongqing 401120, China
Received 1 November 2013; Accepted 17 December 2013
Academic Editor: Khalil Ezzinbi
Copyright © 2013 Xiang-Kai Sun 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.
- F. Giannessi, “Theorems of alternative, quadratic programs and complementarity problems,” in Variational Inequalities and Complementarity Problems, pp. 151–186, John Wiley & Sons, New York, NY, USA, 1980.
- F. Giannessi, Vector Variational Inequalities and Vector Equilibria, vol. 38 of Mathematical Theories, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000.
- G. Y. Chen, X. Huang, and X. Yang, Vector Optimization: Set-Valued and Variational Analysis, vol. 541 of Lecture Notes in Economics and Mathematical Systems, Springer, Berlin, Germany, 2005.
- J. C. Yao, “Variational inequalities with generalized monotone operators,” Mathematics of Operations Research, vol. 19, no. 3, pp. 691–705, 1994.
- J. C. Yao, “Multi-valued variational inequalities with -pseudomonotone operators,” Journal of Optimization Theory and Applications, vol. 83, no. 2, pp. 391–403, 1994.
- S. J. Yu and J. C. Yao, “On vector variational inequalities,” Journal of Optimization Theory and Applications, vol. 89, no. 3, pp. 749–769, 1996.
- L.-C. Zeng and J.-C. Yao, “Existence of solutions of generalized vector variational inequalities in reflexive Banach spaces,” Journal of Global Optimization, vol. 36, no. 4, pp. 483–497, 2006.
- G. Y. Chen and S. J. Li, “Existence of solutions for a generalized vector quasivariational inequality,” Journal of Optimization Theory and Applications, vol. 90, no. 2, pp. 321–334, 1996.
- G. M. Lee, D. S. Kim, B. S. Lee, and N. D. Yen, “Vector variational inequality as a tool for studying vector optimization problems,” Nonlinear Analysis, vol. 34, no. 5, pp. 745–765, 1998.
- I. V. Konnov, “A scalarization approach for vector variational inequalities with applications,” Journal of Global Optimization, vol. 32, no. 4, pp. 517–527, 2005.
- X. Q. Yang and J. C. Yao, “Gap functions and existence of solutions to set-valued vector variational inequalities,” Journal of Optimization Theory and Applications, vol. 115, no. 2, pp. 407–417, 2002.
- G. Y. Chen, C.-J. Goh, and X. Q. Yang, “On gap functions for vector variational inequalities,” in Vector Variational Inequalities and Vector Equilibria, vol. 38 of Mathematical Theories, pp. 55–70, Kluwer Academic, Boston, Mass, USA, 2000.
- S. J. Li and G. Y. Chen, “Properties of gap function for vector variational inequality,” in Variational Analysis and Applications, F. Giannessi and A. Maugeri, Eds., vol. 79, pp. 605–631, Springer, Berlin, Germany, 2005.
- S. J. Li, H. Yan, and G. Y. Chen, “Differential and sensitivity properties of gap functions for vector variational inequalities,” Mathematical Methods of Operations Research, vol. 57, no. 3, pp. 377–391, 2003.
- K. W. Meng and S. J. Li, “Differential and sensitivity properties of gap functions for Minty vector variational inequalities,” Journal of Mathematical Analysis and Applications, vol. 337, no. 1, pp. 386–398, 2008.
- R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, NJ, USA, 1970.
- A. Auslender, Optimisation: Methodes Numeriques, Masson, Paris, France, 1976.