- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Advances in Operations Research
Volume 2012 (2012), Article ID 279215, 13 pages
Generalized -Type I Univex Functions in Multiobjective Optimization
1Department of Mathematics, Dronacharya Government College (DGC), New Railway Road, Gurgaon 122001, India
2Department of Applied Sciences and Humanities, ITM University, Gurgaon 122017, India
3Centre for Mathematical Sciences, Banasthali University, Rajasthan 304022, India
Received 13 March 2012; Revised 5 June 2012; Accepted 11 June 2012
Academic Editor: J. J. Judice
Copyright © 2012 Pallavi Kharbanda 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.
- M. A. Hanson, “On sufficiency of the Kuhn-Tucker conditions,” Journal of Mathematical Analysis and Applications, vol. 80, no. 2, pp. 545–550, 1981.
- F. A. Zhao, “On sufficiency of the Kuhn-Tucker conditions in nondifferentiable programming,” Bulletin of the Australian Mathematical Society, vol. 46, no. 3, pp. 385–389, 1992.
- T. Antczak, “Multiobjective programming under -invexity,” European Journal of Operational Research, vol. 137, no. 1, pp. 28–36, 2002.
- Y. L. Ye, “-invexity and optimality conditions,” Journal of Mathematical Analysis and Applications, vol. 162, no. 1, pp. 242–249, 1991.
- C. R. Bector, S. K. Suneja, and S. Gupta, “Univex functions and univex nonlinear programming,” in Proceeding of the Administrative Sciences Association of Canada, pp. 115–124, 1992.
- N. G. Rueda, M. A. Hanson, and C. Singh, “Optimality and duality with generalized convexity,” Journal of Optimization Theory and Applications, vol. 86, no. 2, pp. 491–500, 1995.
- S. K. Mishra, “On multiple-objective optimization with generalized univexity,” Journal of Mathematical Analysis and Applications, vol. 224, no. 1, pp. 131–148, 1998.
- S. K. Mishra, S.-Y. Wang, and K. K. Lai, “Optimality and duality for multiple-objective optimization under generalized type I univexity,” Journal of Mathematical Analysis and Applications, vol. 303, no. 1, pp. 315–326, 2005.
- A. Jayswal, “On sufficiency and duality in multiobjective programming problem under generalized -type I univexity,” Journal of Global Optimization, vol. 46, no. 2, pp. 207–216, 2010.
- C. Nahak and R. N. Mohapatra, “-invexity in multiobjective optimization,” Nonlinear Analysis, vol. 70, no. 6, pp. 2288–2296, 2009.
- A. Ben-Israel and B. Mond, “What is invexity?” Journal of the Australian Mathematical Society B, vol. 28, no. 1, pp. 1–9, 1986.
- F. H. Clarke, Optimization and Nonsmooth Analysis, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons, New York, NY, USA, 1983.
- K. Miettinen, Nonlinear Multiobjective Optimization, vol. 12 of International Series in Operations Research & Management Science, Kluwer Academic, Boston, Mass, USA, 1999.
- S. K. Mishra, S. Y. Wang, and K. K. Lai, “Optimality and duality in nondifferentiable and multiobjective programming under generalized -invexity,” Journal of Global Optimization, vol. 29, no. 4, pp. 425–438, 2004.
- M. A. Hanson and B. Mond, “Necessary and sufficient conditions in constrained optimization,” Mathematical Programming, vol. 37, no. 1, pp. 51–58, 1987.