Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

SECOND-ORDER SYMMETRIC DUALITY IN MULTIOBJECTIVE PROGRAMMING OVER CONES

  • GULATI, TILAK RAJ (DEPARTMENT OF MATHEMATICS INDIAN INSTITUTE OF TECHNOLOGY ROORKEE) ;
  • MEHNDIRATTA, GEETA (DEPARTMENT OF APPLIED SCIENCES AND HUMANITIES INDIRA GANDHI DELHI TECHNICAL UNIVERSITY FOR WOMEN)
  • Received : 2012.12.26
  • Published : 2016.01.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, some omissions in Mishra and Lai [13], have been pointed out and their corrective measures have been discussed briefly.

Keywords

References

  1. I. Ahmad, Second order symmetric duality in nondifferentiable multiobjective programming, Inform. Sci. 173 (2005), no. 1-3, 23-34. https://doi.org/10.1016/j.ins.2004.06.002
  2. I. Ahmad and Z. Husain, Nondifferentiable second order symmetric duality in multiobjective programming, Appl. Math. Lett. 18 (2005), no. 7, 721-728. https://doi.org/10.1016/j.aml.2004.05.010
  3. M. S. Bazaraa and J. J. Goode, On symmetric duality in nonlinear programming, Operations Res. 21 (1973), 1-9. https://doi.org/10.1287/opre.21.1.1
  4. G. B. Dantzig, E. Eisenberg, and R. W. Cottle, Symmetric dual nonlinear programs, Pacific J. Math. 15 (1965), 809-812. https://doi.org/10.2140/pjm.1965.15.809
  5. G. Devi, Symmetric duality for nonlinear programming problem involving-bonvex functions, European J. Operational Research 104 (1998), 615-621. https://doi.org/10.1016/S0377-2217(97)00020-9
  6. W. S. Dorn, A symmetric dual theorem for quadratic programs, J. Operations Research Society of Japan 2 (1960), 93-97.
  7. T. R. Gulati, S. K. Gupta, and I. Ahmad, Second-order symmetric duality with cone constraints, J. Comput. Appl. Math. 220 (2008), no. 1-2, 347-354. https://doi.org/10.1016/j.cam.2007.08.021
  8. T. R. Gulati and G. Mehndiratta, Nondifferentiable multiobjective Mond-Weir type second-order symmetric duality over cones, Optim. Lett. 4 (2010), no. 2, 293-309. https://doi.org/10.1007/s11590-009-0161-6
  9. S. H. Hou and X. M. Yang, On second-order symmetric duality in nondifferentiable programming, J. Math. Anal. Appl. 255 (2001), no. 2, 491-498. https://doi.org/10.1006/jmaa.2000.7242
  10. S. Khurana, Symmetric duality in multiobjective programming involving generalized cone-index functions, European J. Oper. Res. 165 (2005), no. 3, 592-597. https://doi.org/10.1016/j.ejor.2003.03.004
  11. O. L. Mangasarian, Second and higher-order duality in nonlinear programming, J. Math. Anal. Appl. 51 (1975), no. 3, 607-620. https://doi.org/10.1016/0022-247X(75)90111-0
  12. S. K. Mishra, Multiobjective second order symmetric duality with cone constraints, European J. Oper. Res. 126 (2000), no. 3, 675-682. https://doi.org/10.1016/S0377-2217(99)00339-2
  13. S. K. Mishra and K. K. Lai, Second order symmetric duality in multiobjective program- ming involving generalized cone-invex functions, European J. Oper. Res. 178 (2007), no. 1, 20-26. https://doi.org/10.1016/j.ejor.2005.11.024
  14. S. K. Suneja, S. Aggarwal, and S. Davar, Multiobjective symmetric duality involving cones, European J. Oper. Res. 141 (2002), no. 3, 471-479. https://doi.org/10.1016/S0377-2217(01)00258-2
  15. S. K. Suneja, C. S. Lalitha, and S. Khurana, Second order symmetric duality in multi- objective programming, European J. Oper. Res. 144 (2003), no. 3, 492-500. https://doi.org/10.1016/S0377-2217(02)00154-6
  16. X. M. Yang, X. Q. Yang, K. L. Teo, and S. H. Hou, Multiobjective second-order sym- metric duality with F-convexity, European J. Oper. Res. 165 (2005), no. 3, 585-591. https://doi.org/10.1016/j.ejor.2004.01.028