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Generalized Fritz John optimality in nonlinear programming in the presence of equality and inequality constraints

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  • Hachem Slimani

    (University of Bejaia)

  • Mohammed-Said Radjef

    (University of Bejaia)

Abstract

In this paper, we study Fritz John type optimality conditions for constrained nonlinear programming in which equality and inequality constraints are together present. We introduce a generalized Fritz John condition which is necessary and sufficient for a feasible point to be an optimal solution under weak invexity. In particular, by combining the introduced generalized Fritz John condition with the invexity with respect to different functions, we obtain sufficient optimality conditions which extend and generalize various results in the literature, and their importance and usefulness are illustrated on examples .

Suggested Citation

  • 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.
    • Handle: RePEc:spr:operea:v:16:y:2016:i:2:d:10.1007_s12351-015-0206-9
    DOI: 10.1007/s12351-015-0206-9
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    References listed on IDEAS

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    1. 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.
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    5. 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.
    6. R. Zeng & R. J. Caron, 2006. "Generalized Motzkin Theorems of the Alternative and Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 131(2), pages 281-299, November.
    7. 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.
    8. Birbil, S.I. & Frenk, J.B.G. & Still, G.J., 2007. "An elementary proof of the Fritz-John and Karush-Kuhn-Tucker conditions in nonlinear programming," European Journal of Operational Research, Elsevier, vol. 180(1), pages 479-484, July.
    9. T. Antczak, 2005. "Modified Ratio Objective Approach in Mathematical Programming," Journal of Optimization Theory and Applications, Springer, vol. 126(1), pages 23-40, July.
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