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Multiobjective Fractional Programming Involving Generalized Semilocally V-Type I-Preinvex and Related Functions

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  • Hachem Slimani
  • Shashi Kant Mishra

Abstract

We study a nonlinear multiple objective fractional programming with inequality constraints where each component of functions occurring in the problem is considered semidifferentiable along its own direction instead of the same direction. New Fritz John type necessary and Karush-Kuhn-Tucker type necessary and sufficient efficiency conditions are obtained for a feasible point to be weakly efficient or efficient. Furthermore, a general Mond-Weir dual is formulated and weak and strong duality results are proved using concepts of generalized semilocally V-type I-preinvex functions. This contribution extends earlier results of Preda (2003), Mishra et al. (2005), Niculescu (2007), and Mishra and Rautela (2009), and generalizes results obtained in the literature on this topic.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jijmms:496149
    DOI: 10.1155/2014/496149
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    References listed on IDEAS

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    1. Kaul, R. N. & Kaur, Surjeet, 1982. "Generalizations of convex and related functions," European Journal of Operational Research, Elsevier, vol. 9(4), pages 369-377, April.
    2. Shashi Kant Mishra & Shouyang Wang & Kin Keung Lai, 2008. "V-Invex Functions and Vector Optimization," Springer Optimization and Its Applications, Springer, number 978-0-387-75446-8, December.
    3. Jen-Chwan Liu & Chun-Yu Liu, 2013. "Optimality and Duality for Multiobjective Fractional Programming Involving Nonsmooth Generalized -Univex Functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2013, pages 1-10, November.
    4. 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.
    5. Altannar Chinchuluun & Dehui Yuan & Panos Pardalos, 2007. "Optimality conditions and duality for nondifferentiable multiobjective fractional programming with generalized convexity," Annals of Operations Research, Springer, vol. 154(1), pages 133-147, October.
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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.

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