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Optimality Conditions and Duality for Nondifferentiable Multiobjective Fractional Programming Problems with (C,α,ρ,d)-convexity

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Abstract

The purpose of this paper is to consider a class of nondifferentiable multiobjective fractional programming problems in which every component of the objective function contains a term involving the support function of a compact convex set. Based on the (C,α,ρ,d)-convexity, sufficient optimality conditions and duality results for weakly efficient solutions of the nondifferentiable multiobjective fractional programming problem are established. The results extend and improve the corresponding results in the literature.

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References

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

    Article  MATH  MathSciNet  Google Scholar 

  2. Chandra, S., Craven, B.D., Mond, B.: Vector-valued Lagrangian and multiobjective fractional programming duality. Numer. Funct. Anal. Optim. 11, 239–254 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  3. Chinchuluun, A., Yuan, D.H., Pardalos, P.M.: Optimality conditions and duality for nondifferentiable multiobjective fractional programming with generalized convexity. Ann. Oper. Res. 154, 133–147 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  4. Kim, D.S., Kim, S.J., Kim, M.H.: Optimality and duality for a class of nondifferentiable multiobjective fractional programming problems. J. Optim. Theory Appl. 129, 131–146 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  5. Kuk, H., Lee, G.M., Kim, D.S.: Nonsmooth multiobjective programs with (V,ϱ)-invexity. Ind. J. Pure Appl. Math. 29, 405–412 (1998)

    MATH  MathSciNet  Google Scholar 

  6. Kuk, H., Lee, G.M., Tanina, T.: Optimality and duality for nonsmooth multiobjective fractional programming with generalized invexity. J. Math. Anal. Appl. 262, 365–375 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  7. 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  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  9. Liu, J.C.: Optimality and duality for multiobjective fractional programming involving nonsmooth pseudoinvex functions. Optimization 37, 27–39 (1996)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  11. Liu, S.M., Feng, E.M.: Optimality conditions and duality for a class of nondifferentiable multi-objective fractional programming problems. J. Global Optim. 38, 653–666 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  12. Long, X.J., Huang, N.J., Liu, Z.B.: Optimality conditions, duality and saddle points for nondifferentiable multiobjective fractional programs. J. Ind. Manag. Optim. 4, 287–298 (2008)

    MATH  MathSciNet  Google Scholar 

  13. Mond, B., Schechter, M.: Nondifferentiable symmetric duality. Bull. Aust. Math. Soc. 53, 177–187 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  14. Mukherjee, R.N.: Generalized convex duality for multiobjective fractional programs. J. Math. Anal. Appl. 162, 309–316 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  15. Rreda, V.: On efficiency and duality for multiobjective programs. J. Math. Anal. Appl. 166, 365–377 (1992)

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

  17. Weir, T.: A dual for a multiobjective fractional programming problem. J. Inf. Optim. Sci. 7, 261–269 (1986)

    MATH  MathSciNet  Google Scholar 

  18. Yang, X.M., Teo, K.L., Yang, X.Q.: Duality for a class of nondifferentiable multiobjective programming problems. J. Math. Anal. Appl. 252, 999–1005 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  19. Yuan, D.H., Liu, X.L., Chinchuluun, A., Pardalos, P.M.: Nondifferentiable minimax fractional programming problems with (C,α,ρ,d)-convexity. J. Optim. Theory Appl. 129, 185–199 (2006)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, P.R. China

    X. J. Long

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  1. X. J. Long
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Correspondence to X. J. Long.

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Communicated by P.M. Pardalos.

This work was supported by the National Natural Science Foundation of China (No. 11001287), the Education Committee Project Research Foundation of Chongqing (No. KJ100711), the Natural Science Foundation Project of Chongqing (CSTC 2009BB3372) and the Research Fund of Chongqing Technology and Business University (09-56-06).

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Long, X.J. Optimality Conditions and Duality for Nondifferentiable Multiobjective Fractional Programming Problems with (C,α,ρ,d)-convexity. J Optim Theory Appl 148, 197–208 (2011). https://doi.org/10.1007/s10957-010-9740-z

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