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Nondifferentiable multiobjective programming under generalized dI-invexity

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  • Slimani, Hachem
  • Radjef, Mohammed Said

Abstract

In this paper, we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints. We introduce new concepts of dI-invexity and generalized dI-invexity in which each component of the objective and constraint functions is directionally differentiable in its own direction di. New Fritz-John type necessary and Karush-Kuhn-Tucker type necessary and sufficient optimality conditions are obtained for a feasible point to be weakly efficient, efficient or properly efficient. Moreover, we prove weak, strong, converse and strict duality results for a Mond-Weir type dual under various types of generalized dI-invexity assumptions.

Suggested Citation

  • Slimani, Hachem & Radjef, Mohammed Said, 2010. "Nondifferentiable multiobjective programming under generalized dI-invexity," European Journal of Operational Research, Elsevier, vol. 202(1), pages 32-41, April.
    • Handle: RePEc:eee:ejores:v:202:y:2010:i:1:p:32-41
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    References listed on IDEAS

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    1. Mishra, S. K. & Wang, S. Y. & Lai, K. K., 2005. "Nondifferentiable multiobjective programming under generalized d-univexity," European Journal of Operational Research, Elsevier, vol. 160(1), pages 218-226, January.
    2. Stancu-Minasian, I.M., 2006. "Optimality and duality in nonlinear programming involving semilocally B-preinvex and related functions," European Journal of Operational Research, Elsevier, vol. 173(1), pages 47-58, August.
    3. Suneja, S.K. & Khurana, Seema & Vani, 2008. "Generalized nonsmooth invexity over cones in vector optimization," European Journal of Operational Research, Elsevier, vol. 186(1), pages 28-40, April.
    4. Fulga, C. & Preda, V., 2009. "Nonlinear programming with E-preinvex and local E-preinvex functions," European Journal of Operational Research, Elsevier, vol. 192(3), pages 737-743, February.
    5. Antczak, Tadeusz, 2002. "Multiobjective programming under d-invexity," European Journal of Operational Research, Elsevier, vol. 137(1), pages 28-36, February.
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    1. Hachem Slimani & Mohammed-Said Radjef, 2016. "Generalized Fritz John optimality in nonlinear programming in the presence of equality and inequality constraints," Operational Research, Springer, vol. 16(2), pages 349-364, July.
    2. Hachem Slimani & Shashi Kant Mishra, 2014. "Multiobjective Fractional Programming Involving Generalized Semilocally V-Type I-Preinvex and Related Functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-12, May.
    3. Tadeusz Antczak, 2023. "On directionally differentiable multiobjective programming problems with vanishing constraints," Annals of Operations Research, Springer, vol. 328(2), pages 1181-1212, September.

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