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E-Convex Sets, E-Convex Functions, and E-Convex Programming

Author

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  • E. A. Youness

    (Tanta University)

Abstract

A class of sets and a class of functions called E-convex sets and E-convex functions are introduced by relaxing the definitions of convex sets and convex functions. This kind of generalized convexity is based on the effect of an operator E on the sets and domain of definition of the functions. The optimality results for E-convex programming problems are established.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:102:y:1999:i:2:d:10.1023_a:1021792726715
    DOI: 10.1023/A:1021792726715
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    Citations

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    Cited by:

    1. D. I. Duca & L. Lupşa, 2006. "On the E-Epigraph of an E-Convex Function," Journal of Optimization Theory and Applications, Springer, vol. 129(2), pages 341-348, May.
    2. Dorel Duca & Liana Lupsa, 2012. "Saddle points for vector valued functions: existence, necessary and sufficient theorems," Journal of Global Optimization, Springer, vol. 53(3), pages 431-440, July.
    3. 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.
    4. 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.
    5. Cristescu, Gabriela & Noor, Muhammad Aslam & Noor, Khalida Inayat & Awan, Muhammad Uzair, 2016. "Some inequalities for functions having Orlicz-convexity," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 226-236.
    6. Wedad Saleh & Abdelghani Lakhdari & Ohud Almutairi & Adem Kiliçman, 2023. "Some Remarks on Local Fractional Integral Inequalities Involving Mittag–Leffler Kernel Using Generalized ( E , h )-Convexity," Mathematics, MDPI, vol. 11(6), pages 1-13, March.
    7. Najeeb Abdulaleem, 2021. "Mixed E-duality for E-differentiable Vector Optimization Problems Under (Generalized) V-E-invexity," SN Operations Research Forum, Springer, vol. 2(3), pages 1-18, September.
    8. Tadeusz Antczak & Najeeb Abdulaleem, 2023. "On the exactness and the convergence of the $$l_{1}$$ l 1 exact penalty E-function method for E-differentiable optimization problems," OPSEARCH, Springer;Operational Research Society of India, vol. 60(3), pages 1331-1359, September.
    9. Muhammad Adil Khan & Asadullah Sohail & Hidayat Ullah & Tareq Saeed, 2023. "Estimations of the Jensen Gap and Their Applications Based on 6-Convexity," Mathematics, MDPI, vol. 11(8), pages 1-25, April.
    10. 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.

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