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Multiobjective Variational Programming under Generalized Type I Univexity

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Abstract

In this paper, we extend the Mishra, Rueda and Giorgi generalized V-univexity type I, defined for multiobjective programming, to multiobjective variational programming problems and we derive various sufficient optimality conditions and mixed type duality results under generalized V-univexity type I conditions.

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References

  1. Chinchuluun, A., Pardalos, P.M.: Multiobjective programming problems under generalized convexity. In: Torn, A., Zilinskas, J. (eds.) Models and Algorithms for Global Optimization, pp. 3–20. Springer, Berlin (2006)

    Google Scholar 

  2. Mond, B., Hanson, M.A.: Duality for variational problems. J. Math. Anal. Appl. 18, 355–364 (1967)

    Article  MATH  MathSciNet  Google Scholar 

  3. Mishra, S.K., Wang, S.Y., Lai, K.K.: V-Invex Functions and Vector Optimization. Springer Optimization and Its Applications, vol. 14. Springer, Berlin (2008)

    MATH  Google Scholar 

  4. Bector, C.R., Husain, I.: Duality for multiobjective variational problems. J. Math. Anal. Appl. 166, 214–229 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  5. Aghezzaf, B., Hachimi, M.: Generalized invexity and duality in multiobjective programming problems. J. Glob. Optim. 18, 91–101 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  6. Aghezzaf, B., Hachimi, M.: Sufficiency and duality in multiobjective variational problems with generalized type I functions. J. Glob. Optim. 34, 191–218 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  7. Nahak, C., Nanda, C.: Duality for multiobjective variational problems with invexity. Optimization 36, 235–248 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  8. Mond, B., Chandra, S., Husain, I.: Duality for variational problems with invexity. J. Math. Anal. Appl. 134, 322–328 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  9. Bhatia, D., Kumar, P.: Duality for multiobjective variational problems with B-vex functions. Optimization 36, 347–360 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  10. Bhatia, D., Mehra, A.: Optimality conditions and duality for multiobjective variational problems with generalized B-invexity. J. Math. Anal. Appl. 234, 341–360 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  11. Mukherjee, R.N., Purnachandra Rao, C.: Mixed type duality for multiobjective variational problems. J. Math. Anal. Appl. 252, 571–586 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  12. Aghezzaf, B., Khazafi, K.: Sufficient optimality conditions and duality in multiobjective variational programming problems with generalized b-invexity. J. Control Cyber. 33, 1–14 (2004)

    MathSciNet  Google Scholar 

  13. Mishra, S.K., Rueda, N.G., Giorgi, G.: Multiobjective programming under generalized type I univexity. An. Univ. Bucur. Mat. 52, 207–224 (2003)

    MATH  MathSciNet  Google Scholar 

  14. Valentine, F.A.: The Problem of Lagrange with Differentiable Inequalities as Added Side Constraints, Contribution to the Calculus of Variation, 1933–1937. University of Chicago Press, Chicago (1937), pp. 407–448

    Google Scholar 

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Authors and Affiliations

  1. Kent State University, Kent, 44240, OH, USA

    K. Khazafi

  2. Merrimack College, North Andover, 01845, MA, USA

    N. Rueda

Authors
  1. K. Khazafi
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  2. N. Rueda
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Corresponding author

Correspondence to K. Khazafi.

Additional information

Communicated by P.M. Pardalos.

The authors thank the referee for many valuable comments and helpful suggestions.

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Khazafi, K., Rueda, N. Multiobjective Variational Programming under Generalized Type I Univexity. J Optim Theory Appl 142, 363–376 (2009). https://doi.org/10.1007/s10957-009-9526-3

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