Skip to main content
Log in

Second order symmetric duality in nondifferentiable multiobjective fractional programming with cone convex functions

  • Original Research
  • Published:
Journal of Applied Mathematics and Computing Aims and scope Submit manuscript

Abstract

In the present paper, we consider Mond-Weir type nondifferentiable second order fractional symmetric dual programs over arbitrary cones and derive duality results under second order KF-convexity/KF-pseudoconvexity assumptions. Our results generalize several known results in the literature.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Ahmad, I.: Second order symmetric duality in nondifferentiable multiobjective programming. Inf. Sci. 173, 23–34 (2005)

    Article  MATH  Google Scholar 

  2. Ahmad, I., Husain, Z.: Second order symmetric duality in multiobjective programming involving cones. Optim. Lett. 7, 1353–1365 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  3. Ahmad, I., Husain, Z.: Nondifferentiable second order symmetric duality in multiobjective programming. Appl. Math. Lett. 18, 721–728 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  4. Ahmad, I., Sharma, S.: Multiobjective fractional symmetric duality involving cones. J. Appl. Math. Inform. 26, 151–160 (2008)

    Google Scholar 

  5. Bazaraa, M.S., Goode, J.J.: On symmetric duality in nonlinear programming. Oper. Res. 21, 1–9 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  6. Dorn, W.S.: A symmetric dual theorem for quadratic programs. J. Oper. Res. Soc. Jpn. 2, 93–97 (1960)

    Google Scholar 

  7. Gulati, T.R., Mehndiratta, G.: Nondifferentiable multiobjective Mond-Weir type second-order symmetric duality over cones. Optim. Lett. 4, 293–309 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  8. Gulati, T.R., Mehndiratta, G., Verma, K.: Symmetric duality for second-order fractional programs. Optim. Lett. 7, 1341–1352 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  9. Gupta, S.K., Kailey, N.: Nondifferentiable multiobjective second-order symmetric duality. Optim. Lett. 5, 125–139 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  10. Gupta, S.K., Kailey, N., Sharma, M.K.: Mond-Weir type nondifferentiable multiobjective second-order symmetric duality with cone constraints. Int. J. Math. Oper. Res. 3, 414–430 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  11. Hanson, M.A.: On sufficiency of Kuhn-Tucker conditions. J. Math. Anal. Appl. 80, 545–550 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  12. Hanson, M.A., Mond, B.: Further generalizations of convexity in mathematical programming. J. Inf. Optim. Sci. 3, 25–32 (1982)

    MATH  MathSciNet  Google Scholar 

  13. Kailey, N., Gupta, S.K., Danger, D.: Mixed second-order multiobjective symmetric duality with cone constraints. Nonlinear Anal., Real World Appl. 12, 3373–3383 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  14. Abd El-H. Kassem, M.: Multiobjective nonlinear second order symmetric duality with (K,F)-pseudoconvexity. Appl. Math. Comput. 219, 2142–2148 (2012)

    Article  MathSciNet  Google Scholar 

  15. Khurana, S.: Symmetric duality in multiobjective programming involving generalized cone-invex functions. Eur. J. Oper. Res. 165, 592–597 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  16. Kim, D.S., Lee, H.J., Lee, Y.J.: Generalized second order symmetric duality in nondifferentiable multiobjective programming. Taiwan. J. Math. 11, 745–764 (2007)

    MATH  Google Scholar 

  17. Kim, D.S., Yun, Y.B., Lee, W.J.: Multiobjective symmetric duality with cone constraints. Eur. J. Oper. Res. 107, 686–691 (1998)

    Article  MATH  Google Scholar 

  18. Ojha, D.B.: On second-order symmetric duality for a class of multiobjective fractional programming problem. Tamkang J. Math. 43, 267–279 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  19. Stancu-Minasian, I.M.: Fractional Programming: Theory, Methods and Applications. Kluwer, Dordrecht (1997)

    Book  MATH  Google Scholar 

  20. Stancu-Minasian, I.M.: A sixth bibliography of fractional programming. Optimization 55, 405–428 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  21. Stancu-Minasian, I.M.: A seventh bibliography of fractional programming. Adv. Model. Optim. 15, 309–386 (2013)

    Google Scholar 

  22. Mond, B., Schechter, M.: Non-differentiable symmetric duality. Bull. Aust. Math. Soc. 53, 177–188 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  23. Mond, B., Weir, T.: Generalized concavity and duality. In: Schaible, S., Ziemba, W.T. (eds.) Generalized Concavity in Optimization and Economics, pp. 263–280. Academic Press, New York (1981)

    Google Scholar 

  24. Schechter, M.: More on subgradient duality. J. Math. Anal. Appl. 71, 251–262 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  25. Suneja, S.K., Aggarwal, S., Davar, S.: Multiobjective symmetric duality involving cones. Eur. J. Oper. Res. 141, 471–479 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  26. Suneja, S.K., Lalitha, C.S., Khurana, S.: Second order symmetric duality in multiobjective programming. Eur. J. Oper. Res. 144, 492–500 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  27. Yang, X.M., Yang, X.Q., Teo, K.L., Hou, S.H.: Second order symmetric duality in non-differentiable multiobjective programming with F-convexity. Eur. J. Oper. Res. 164, 406–416 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  28. Ying, G.: Higher-order symmetric duality for a class of multiobjective fractional programming problems. J. Inequal. Appl., 142 (2012)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Anurag Jayswal.

Additional information

The research of the first author is financially supported by the University Grant Commission, New Delhi, India through grant no. (F. No. 41-801/2012 (SR)).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jayswal, A., Kumar Prasad, A. Second order symmetric duality in nondifferentiable multiobjective fractional programming with cone convex functions. J. Appl. Math. Comput. 45, 15–33 (2014). https://doi.org/10.1007/s12190-013-0708-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12190-013-0708-7

Keywords

Mathematics Subject Classification (2010)

Navigation