Table of Contents
ISRN Applied Mathematics
Volume 2014 (2014), Article ID 687917, 10 pages
http://dx.doi.org/10.1155/2014/687917
Research Article

Wolfe Type Second Order Nondifferentiable Symmetric Duality in Multiobjective Programming over Cone with Generalized (K, F)-Convexity

Department of Mathematics, Trident Academy of Technology, Chandaka Industrial Estate, F2/A, Bhubaneswar, Odisha 751024, India

Received 2 January 2014; Accepted 6 February 2014; Published 24 April 2014

Academic Editors: F. Ding and F. Zirilli

Copyright © 2014 A. K. Tripathy. 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

  1. V. Pareto, Course D‘economic Politique, Lausanne, Raye, Saint Lucia, 1986.
  2. H. W. Kuhn and A. W. Tucker, “Nonlinear programming,” in Proceedings of the 2nd Berkeley Symposium on Mathematical Statistics and Probability, pp. 481–492, University of California Press, Berkeley, Calif, USA, 1951. View at MathSciNet
  3. A. M. Geoffrion, “Proper efficiency and the theory of vector maximization,” Journal of Mathematical Analysis and Applications, vol. 22, pp. 618–630, 1968. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. W. S. Dorn, “A symmetric dual theorem for quadratic programs,” Journal of the Operations Research Society of Japan, vol. 2, pp. 93–97, 1960. View at Google Scholar
  5. G. B. Dantzig, E. Eisenberg, and R. W. Cottle, “Symmetric dual nonlinear programs,” Pacific Journal of Mathematics, vol. 15, pp. 809–812, 1965. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. B. Mond, “Second order duality for nonlinear programs,” Opsearch, vol. 11, no. 2-3, pp. 90–99, 1974. View at Google Scholar · View at MathSciNet
  7. B. Mond and T. Weir, “Generalized concavity and duality,” in Generalized Concavity in Optimization and Economics, S. Schaible and W. T. Ziemba, Eds., pp. 263–279, Academic Press, New York, NY, USA, 1981. View at Google Scholar · View at Zentralblatt MATH
  8. O. L. Mangasarian, “Second- and higher-order duality in nonlinear programming,” Journal of Mathematical Analysis and Applications, vol. 51, no. 3, pp. 607–620, 1975. View at Publisher · View at Google Scholar · View at MathSciNet
  9. C. R. Bector and S. Chandra, “Generalized bonvex function and second order duality in mathematical programming,” Research Report 85-2, The University of Manitoba, Winnipeg, Canada, 1985. View at Google Scholar
  10. G. Devi, “Symmetric duality for nonlinear programming problem involving η-bonvex functions,” European Journal of Operational Research, vol. 104, no. 3, pp. 615–621, 1998. View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. S. Khurana, “Symmetric duality in multiobjective programming involving generalized cone-index functions,” European Journal of Operational Research, vol. 165, no. 3, pp. 592–597, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  12. X. M. Yang, X. Q. Yang, K. L. Teo, and S. H. Hou, “Second order symmetric duality in non-differentiable multiobjective programming with F-convexity,” European Journal of Operational Research, vol. 164, no. 2, pp. 406–416, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. X. M. Yang, X. Q. Yang, K. L. Teo, and S. H. Hou, “Multiobjective second-order symmetric duality with F-convexity,” European Journal of Operational Research, vol. 165, no. 3, pp. 585–591, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. T. R. Gulati, S. K. Gupta, and I. Ahmad, “Second-order symmetric duality with cone constraints,” Journal of Computational and Applied Mathematics, vol. 220, no. 1-2, pp. 347–354, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. T. R. Gulati and Geeta, “Mond-Weir type second-order symmetric duality in multiobjective programming over cones,” Applied Mathematics Letters, vol. 23, no. 4, pp. 466–471, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. T. R. Gulati and K. Verma, “Nondifferentiable multiobjective Wolfe type symmetric duality under invexity,” in Proceedings of the International Conference on Soft Computing for Problem Solving, vol. 1, pp. 347–354, 2012.
  17. S. K. Gupta and N. Kailey, “Nondifferentiable multiobjective second-order symmetric duality,” Optimization Letters, vol. 5, no. 1, pp. 125–139, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. S. K. Gupta and N. Kailey, “Second-order multiobjective symmetric duality involving cone-bonvex functions,” Journal of Global Optimization, vol. 55, no. 1, pp. 125–140, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. H. Saini and T. R. Gulati, “Nondifferentiable multiobjective symmetric duality with F-convexity over cones,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 5, pp. 1577–1584, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. M. S. Bazaraa and J. J. Goode, “On symmetric duality in nonlinear programming,” Operations Research, vol. 21, pp. 1–9, 1973. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet