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Nonlinear programming with E-preinvex and local E-preinvex functions


  • Fulga, C.
  • Preda, V.


In this paper, we extend the class of E-convex sets, E-convex and E-quasiconvex functions introduced by [Youness, E.A., 1999. E-convex sets, E-convex functions and E-convex programming. Journal of Optimization Theory and Applications 102, 439-450], respectively by [Syau, Yu-Ru, Lee, E. Stanley, 2005. Some properties of E-convex functions. Applied Mathematics Letters 18, 1074-1080] to E-invex set, E-preinvex, E-prequasiinvex and corresponding local concepts. Some properties of these classes are studied. As an application of our results, we consider the nonlinear programming problem for which, we establish that, under mild conditions, a local minimum is a global minimum.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:192:y:2009:i:3:p:737-743

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    References listed on IDEAS

    1. Antczak, Tadeusz, 2004. "(p,r)-Invexity in multiobjective programming," European Journal of Operational Research, Elsevier, vol. 152(1), pages 72-87, 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. 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.
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    Cited by:

    1. 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.


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