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

Author

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  • X. M. Yang

    (Chongqing Normal University)

Abstract

Recently, E-convex sets and E-convex functions were introduced in Ref. 1. However, some results seem to be incorrect. In this note, some counterexamples are given.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:109:y:2001:i:3:d:10.1023_a:1017532225395
    DOI: 10.1023/A:1017532225395
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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. Rongbo Wang & Qiang Feng, 2024. "Optimality and Duality of Semi-Preinvariant Convex Multi-Objective Programming Involving Generalized ( F , α , ρ , d )- I -Type Invex Functions," Mathematics, MDPI, vol. 12(16), pages 1-13, August.
    6. 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.
    7. Ohud Almutairi & Adem Kılıçman, 2019. "Generalized Integral Inequalities for Hermite–Hadamard-Type Inequalities via s -Convexity on Fractal Sets," Mathematics, MDPI, vol. 7(11), pages 1-16, November.

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