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Higher Order Fractional Symmetric Duality Over Cone Constraints

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Journal of Mathematical Modelling and Algorithms in Operations Research

Abstract

In this paper, a pair of Mond-Weir type higher order fractional symmetric dual program over cone constraints is formulated. Under higher order invexity assumptions, we prove weak, strong and strict duality theorems. Moreover, a self dual program is formulated and self duality theorem is discussed.

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References

  1. Agarwal, R. P., Ahmad, I., Gupta, S. K., Kailey, N.: Generalized second-order mixed symmetric duality in nondifferentiable mathematical programming. Abst. Appl. Anal. 2011 (2011). Article ID 103597

  2. Agarwal, R. P., Ahmad, I., Gupta, S. K.: A note on higher-order nondifferentiable symmetric duality in multiobjective programming. Appl. Math. Lett. 24, 1308–1311 (2011)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  5. Chandra, S., Craven, B. D., Mond, B.: Symmetric dual fractional programming. Z. Oper. Res. 29, 59–64 (1985)

    MATH  MathSciNet  Google Scholar 

  6. Chandra, S., Kumar, V.: A note on pseudo-invexity and symmetric duality. Eur. J. Oper. Res. 105, 626–629 (1988)

    Article  Google Scholar 

  7. Chen, X.: Higher-order symmetric duality in nondifferentiable multiobjective programming problems. J. Math. Anal. Appl. 290, 423–435 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  8. Dantzig, G. B., Eisenberg, E., Cottle, R. W.: Symmetric dual nonlinear programming. Pac. J. Math. 15, 809–812 (1965)

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  10. Gulati, T. R., Ahmad, I., Second-order symmetric duality for minimax mixed integer programs. Eur. J. Oper. Res. 101, 122–129 (1997)

    Article  MATH  Google Scholar 

  11. Gulati, T. R., Ahmad, I., Husain, I.: Second-order symmetric duality with generalized convexity. Opsearch 38, 210–222 (2001)

    MATH  MathSciNet  Google Scholar 

  12. Gulati, T. R., Gupta, S. K., Ahmad, I.: Second order symmetric duality with cone constraints. J. Comp. Appl. Math. 220, 347–354 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  13. Gulati, T. R., Gupta, S. K.: Higher-order symmetric duality with cone constraints. Appl. Math. Lett. 22, 776–781 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  14. 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 

  15. Kassem, M.A. El-H: Symmetric and self duality in vector optimization problem. Appl. Math. Comput. 183, 1121–1126 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  16. Kassem, M.A. El-H: Higher-order symmetric duality in vector optimization problem involving generalized cone-invex functions. Appl. Math. Comp. 209, 405–409 (2009)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  18. Mangasarian, O. L.: Second and higher-order duality in nonlinear programming. J. Math. Anal. Appl. 51, 607–620 (1975)

    Article  MathSciNet  Google Scholar 

  19. 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 

  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. AMO-Adv. Model. Optim. 15, 309–386 (2013)

    Google Scholar 

  22. Stancu Minasian, I. M.: Fractional programming: Theory, Methods, and Applications. Kluwer Academic, Dordrecht (1997)

    Book  MATH  Google Scholar 

  23. Yang, X.M.: On symmetric and self duality in vector optimization problem. J. Indus. Manag. Optim. 7, 523–529 (2011)

    Article  MATH  Google Scholar 

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Correspondence to Anurag Jayswal.

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Jayswal, A., Ahmad, I. & Prasad, A.K. Higher Order Fractional Symmetric Duality Over Cone Constraints. J Math Model Algor 14, 91–101 (2015). https://doi.org/10.1007/s10852-014-9259-7

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  • DOI: https://doi.org/10.1007/s10852-014-9259-7

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