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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 168172, 12 pages
doi:10.1155/2012/168172
Research Article
A Class of -Semipreinvex Functions and Optimality
1Department of Mathematics, Chongqing Normal University, Chongqing 400047, China
2School of Economics and Management, Tsinghua University, Beijing 100084, China
Received 31 May 2012; Accepted 27 October 2012
Academic Editor: Xue-Xiang Huang
Copyright © 2012 Xue Wen Liu 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.
Linked References
- S. Schaible and W. T. Ziemba, Generalized Concavity in Optimization and Economics, Academic Press, London, UK, 1981.
- M. A. Hanson, “On sufficiency of the Kuhn-Tucker conditions,” Journal of Mathematical Analysis and Applications, vol. 80, no. 2, pp. 545–550, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- A. Ben-Israel and B. Mond, “What is invexity?” Bulletin of Australian Mathematical Society B, vol. 28, no. 1, pp. 1–9, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- T. Weir and B. Mond, “Pre-invex functions in multiple objective optimization,” Journal of Mathematical Analysis and Applications, vol. 136, no. 1, pp. 29–38, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- T. Weir and V. Jeyakumar, “A class of nonconvex functions and mathematical programming,” Bulletin of the Australian Mathematical Society, vol. 38, no. 2, pp. 177–189, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- R. Pini, “Invexity and generalized convexity,” Optimization, vol. 22, no. 4, pp. 513–525, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- D. Bhatia and P. Kumar, “Multiobjective control problem with generalized invexity,” Journal of Mathematical Analysis and Applications, vol. 189, no. 3, pp. 676–692, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- S. R. Mohan and S. K. Neogy, “On invex sets and preinvex functions,” Journal of Mathematical Analysis and Applications, vol. 189, no. 3, pp. 901–908, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- L. V. Reddy and R. N. Mukherjee, “Some results on mathematical programming with generalized ratio invexity,” Journal of Mathematical Analysis and Applications, vol. 240, no. 2, pp. 299–310, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- X. M. Yang and D. Li, “On properties of preinvex functions,” Journal of Mathematical Analysis and Applications, vol. 256, no. 1, pp. 229–241, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- D. S. Kim and S. Schaible, “Optimality and duality for invex nonsmooth multiobjective programming problems,” Optimization, vol. 53, no. 2, pp. 165–176, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- T. Antczak, “-preinvexity and -invexity in mathematical programming,” Computers & Mathematics with Applications, vol. 50, no. 3-4, pp. 551–566, 2005. View at Publisher · View at Google Scholar
- T. Antczak, “-invex sets and functions,” Journal of Mathematical Analysis and Applications, vol. 263, no. 2, pp. 355–379, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- T. Antczak, “A class of --invex functions and mathematical programming,” Journal of Mathematical Analysis and Applications, vol. 286, no. 1, pp. 187–206, 2003. View at Publisher · View at Google Scholar
- X. Q. Yang and G. Y. Chen, “A class of nonconvex functions and pre-variational inequalities,” Journal of Mathematical Analysis and Applications, vol. 169, no. 2, pp. 359–373, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- X. M. Yang, X. Q. Yang, and K. L. Teo, “On properties of semipreinvex functions,” Bulletin of the Australian Mathematical Society, vol. 68, no. 3, pp. 449–459, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- T. Antczak, “-pre-invex functions in mathematical programming,” Journal of Computational and Applied Mathematics, vol. 10, pp. 1–15, 2007.
- X. J. Long and J. W. Peng, “Semi-B-preinvex functions,” Journal of Optimization Theory and Applications, vol. 131, no. 2, pp. 301–305, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- K. Q. Zhao, X. W. Liu, and Z. Chen, “A class of -semipreinvex functions and optimality in nonlinear programming,” Journal of Global Optimization, vol. 49, no. 1, pp. 37–47, 2011. View at Publisher · View at Google Scholar