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Multiobjective fractional programming problems involving (p,r)−ρ−(η,θ)-invex function

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Abstract

In this paper we move forward in the study of multiobjective fractional programming problem and established sufficient optimality conditions under the assumption of (p,r)−ρ−(η,θ)-invexity. Weak, strong and strict converse duality theorems are also derived for three type of dual models related to multiobjective fractional programming problem involving aforesaid invex function.

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References

  1. Antczak, T.: (p,r)-invex sets and functions. J. Math. Anal. Appl. 263, 355–379 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bector, C.R., Chandra, S. Husain, I.: Optimality conditions and subdifferentiable multiobjective fractional programming. J. Optim. Theory Appl. 79, 105–125 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chen, X.H.: Optimality and duality for the multiobjective fractional programming with generalized (F,ρ)-convexity. J. Math. Anal. Appl. 273, 190–205 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. Gulati, T.R., Ahmad, I.: Efficiency and duality in multiobjective fractional programming. Opsearch 32, 31–43 (1995)

    MathSciNet  MATH  Google Scholar 

  5. Gulati, T.R., Ahmad, I.: Multiobjective duality using Fritz John conditions. Asia-Pac. J. Oper. Res. 15, 63–74 (1998)

    MathSciNet  MATH  Google Scholar 

  6. Gulati, T.R., Ahmad, I., Agarwal, D.: Sufficiency and duality in multiobjective programming under generalized type I functions. J. Optim. Theory Appl. 135, 411–427 (2007)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  8. Liang, Z.A., Huang, H.X., Pardalos, P.M.: Optimality conditions and duality for a class of nonlinear fractional programming problems. J. Optim. Theory Appl. 110, 611–619 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. Liang, Z.A., Huang, H.X., Pardalos, P.M.: Efficiency conditions and duality for a class of multiobjective fractional programming problems. J. Glob. Optim. 27, 447–471 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  10. Liu, J.C.: Optimality and duality for multiobjective fractional programming involving nonsmooth (F,ρ)-convex functions. Optimization 36, 333–346 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  11. Mandal, P., Nahak, C.: Symmetric duality with (p,r)−ρ−(η,θ)-invexity. Appl. Math. Comput. 217, 8141–8148 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  12. Mukherjee, R.N., Rao, C.P.: Multiobjective fractional programming under generalized invexity. Indian J. Pure Appl. Math. 27, 1175–1183 (1996)

    MathSciNet  MATH  Google Scholar 

  13. Schaible, S.: Fractional programming: applications and algorithms. Eur. J. Oper. Res. 7, 111–120 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  14. Schaible, S.: Fractional programming. In: Horst, R., Pardalos, P. M. (eds.), Handbook of Global Optimization, pp. 495–608. Kluwer Academic, Dordrecht (1995)

    Google Scholar 

  15. Singh, C.: Optimality conditions in multiobjective differentiable programming. J. Optim. Theory Appl. 53, 115–123 (1987)

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  17. Stancu-Minasian, I.M.: A fifth bibliography of fractional programming. Optimization 45, 343–367 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  18. Weir, T.: A duality theorem for a multiobjective fractional optimization problem. Bull. Aust. Math. Soc. 34, 415–425 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  19. Zalmai, G.J.: Generalized sufficiency criteria in continuous-time programming with application to a class of variational-type inequalities. J. Math. Anal. Appl. 153, 331–355 (1990)

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Anurag Jayswal.

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The research of the first author is partially supported by the Indian School of Mines, Dhanbad, under FRS(17)/2010-2011/AM.

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Jayswal, A., Kumar, R. & Kumar, D. Multiobjective fractional programming problems involving (p,r)−ρ−(η,θ)-invex function. J. Appl. Math. Comput. 39, 35–51 (2012). https://doi.org/10.1007/s12190-011-0508-x

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  • DOI: https://doi.org/10.1007/s12190-011-0508-x

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Mathematics Subject Classification (2000)2010

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