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

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  • Fulga, C.
  • Preda, V.

Abstract

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.

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  • 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

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    1. E. A. Youness, 1999. "E-Convex Sets, E-Convex Functions, and E-Convex Programming," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 439-450, August.
    2. X. M. Yang, 2001. "On E-Convex Sets, E-Convex Functions, and E-Convex Programming," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 699-704, June.
    3. Antczak, Tadeusz, 2004. "(p,r)-Invexity in multiobjective programming," European Journal of Operational Research, Elsevier, vol. 152(1), pages 72-87, January.
    4. 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.
    5. 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. Babli Kumari & Anurag Jayswal, 2018. "Some properties of geodesic E-preinvex function and geodesic semi E-preinvex function on Riemannian manifolds," OPSEARCH, Springer;Operational Research Society of India, vol. 55(3), pages 807-822, November.
    2. Akhlad Iqbal & Shahid Ali & I. Ahmad, 2012. "On Geodesic E-Convex Sets, Geodesic E-Convex Functions and E-Epigraphs," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 239-251, October.
    3. 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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