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Some properties of geodesic E-preinvex function and geodesic semi E-preinvex function on Riemannian manifolds

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  • Babli Kumari

    (Indian Institute of Technology (Indian School of Mines))

  • Anurag Jayswal

    (Indian Institute of Technology (Indian School of Mines))

Abstract

In the present paper, the notion of geodesic E-preinvex function and geodesic semi E-preinvex function are introduced on Riemannian manifold. Moreover, several properties, results and relations are studied within aforesaid functions. An example is also constructed to illustrate the definition of geodesic E-preinvex function. In addition, we have studied the optimality results with the help of geodesic E-preinvex and geodesic semi E-preinvex functions.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:opsear:v:55:y:2018:i:3:d:10.1007_s12597-018-0346-9
    DOI: 10.1007/s12597-018-0346-9
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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. 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.
    4. 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.
    5. 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.
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