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On multiobjective second order symmetric duality with cone constraints

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  • Ahmad, I.
  • Husain, Z.

Abstract

A pair of Wolfe type multiobjective second order symmetric dual programs with cone constraints is formulated and usual duality results are established under second order invexity assumptions. These results are then used to investigate symmetric duality for minimax version of multiobjective second order symmetric dual programs wherein some of the primal and dual variables are constrained to belong to some arbitrary sets, i.e., the sets of integers. This paper points out certain omissions and inconsistencies in the earlier work of Mishra [S.K. Mishra, Multiobjective second order symmetric duality with cone constraints, European Journal of Operational Research 126 (2000) 675-682] and Mishra and Wang [S.K. Mishra, S.Y. Wang, Second order symmetric duality for nonlinear multiobjective mixed integer programming, European Journal of Operational Research 161 (2005) 673-682].

Suggested Citation

  • Ahmad, I. & Husain, Z., 2010. "On multiobjective second order symmetric duality with cone constraints," European Journal of Operational Research, Elsevier, vol. 204(3), pages 402-409, August.
    • Handle: RePEc:eee:ejores:v:204:y:2010:i:3:p:402-409
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    References listed on IDEAS

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    1. Kim, Do Sang & Song, Young Ran, 2001. "Minimax and symmetric duality for nonlinear multiobjective mixed integer programming," European Journal of Operational Research, Elsevier, vol. 128(2), pages 435-446, January.
    2. 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.
    3. Mishra, S. K. & Wang, S. Y., 2005. "Second order symmetric duality for nonlinear multiobjective mixed integer programming," European Journal of Operational Research, Elsevier, vol. 161(3), pages 673-682, March.
    4. Nanda, S. & Das, L. N., 1994. "Pseudo-invexity and symmetric duality in nonlinear fractional programming," European Journal of Operational Research, Elsevier, vol. 73(3), pages 577-582, March.
    5. 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.
    6. Chandra, S. & Kumar, V., 1998. "A note on pseudo-invexity and symmetric duality," European Journal of Operational Research, Elsevier, vol. 105(3), pages 626-629, March.
    7. 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.
    8. M. S. Bazaraa & J. J. Goode, 1973. "On Symmetric Duality in Nonlinear Programming," Operations Research, INFORMS, vol. 21(1), pages 1-9, February.
    9. Kim, Moon Hee & Kim, Do Sang, 2008. "Non-differentiable symmetric duality for multiobjective programming with cone constraints," European Journal of Operational Research, Elsevier, vol. 188(3), pages 652-661, August.
    10. 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.
    11. Gulati, T. R. & Ahmad, Izhar, 1997. "Second order symmetric duality for nonlinear minimax mixed integer programs," European Journal of Operational Research, Elsevier, vol. 101(1), pages 122-129, August.
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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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