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Second-order multiobjective symmetric duality with cone constraints

Author

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  • Gulati, T.R.
  • Saini, Himani
  • Gupta, S.K.

Abstract

In this paper, we formulate Wolfe and Mond-Weir type second-order multiobjective symmetric dual problems over arbitrary cones. Weak, strong and converse duality theorems are established under [eta]-bonvexity/[eta]-pseudobonvexity assumptions. This work also removes several omissions in definitions, models and proofs for Wolfe type problems studied in Mishra [9]. Moreover, self-duality theorems for these pairs are obtained assuming the function involved to be skew symmetric.

Suggested Citation

  • Gulati, T.R. & Saini, Himani & Gupta, S.K., 2010. "Second-order multiobjective symmetric duality with cone constraints," European Journal of Operational Research, Elsevier, vol. 205(2), pages 247-252, September.
    • Handle: RePEc:eee:ejores:v:205:y:2010:i:2:p:247-252
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    References listed on IDEAS

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    1. Yang, X. M. & Yang, X. Q. & Teo, K. L. & Hou, S. H., 2005. "Multiobjective second-order symmetric duality with F-convexity," European Journal of Operational Research, Elsevier, vol. 165(3), pages 585-591, September.
    2. Yang, X. M. & Yang, X. Q. & Teo, K. L. & Hou, S. H., 2005. "Second order symmetric duality in non-differentiable multiobjective programming with F-convexity," European Journal of Operational Research, Elsevier, vol. 164(2), pages 406-416, July.
    3. Suneja, S. K. & Aggarwal, Sunila & Davar, Sonia, 2002. "Multiobjective symmetric duality involving cones," European Journal of Operational Research, Elsevier, vol. 141(3), pages 471-479, September.
    4. Devi, G., 1998. "Symmetric duality for nonlinear programming problem involving [eta]-bonvex functions," European Journal of Operational Research, Elsevier, vol. 104(3), pages 615-621, February.
    5. Mishra, S. K., 2000. "Multiobjective second order symmetric duality with cone constraints," European Journal of Operational Research, Elsevier, vol. 126(3), pages 675-682, November.
    6. Suneja, S. K. & Lalitha, C. S. & Khurana, Seema, 2003. "Second order symmetric duality in multiobjective programming," European Journal of Operational Research, Elsevier, vol. 144(3), pages 492-500, February.
    7. Mishra, S. K., 2000. "Second order symmetric duality in mathematical programming with F-convexity," European Journal of Operational Research, Elsevier, vol. 127(3), pages 507-518, December.
    8. Yang, X. M. & Yang, X. Q. & Teo, K. L., 2003. "Non-differentiable second order symmetric duality in mathematical programming with F-convexity," European Journal of Operational Research, Elsevier, vol. 144(3), pages 554-559, February.
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    Cited by:

    1. S. Gupta & N. Kailey, 2013. "Second-order multiobjective symmetric duality involving cone-bonvex functions," Journal of Global Optimization, Springer, vol. 55(1), pages 125-140, January.
    2. C. Zălinescu, 2016. "On Second-Order Generalized Convexity," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 802-829, March.

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