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On Second-Order Generalized Convexity

Author

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  • C. Zălinescu

    (University Alexandru Ioan Cuza
    Romanian Academy)

Abstract

Second-order convex functions were introduced by Mond (Opsearch 11(2–3):90–99, 1974) in order to deal with second-order duality. Then that notion was generalized again and again, using more and more parameters introduced using several quantifiers. In the present paper, we show that most of these notions have quite simple intrinsic characterizations. This paper can be viewed as a continuation of our paper (Zălinescu in An Ştiinţ Univ Al I Cuza Iaşi Secţ I a Mat 35(3):213–220, 1989) in which we characterized generalized bonvex functions.

Suggested Citation

  • C. Zălinescu, 2016. "On Second-Order Generalized Convexity," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 802-829, March.
    • Handle: RePEc:spr:joptap:v:168:y:2016:i:3:d:10.1007_s10957-015-0820-y
    DOI: 10.1007/s10957-015-0820-y
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    References listed on IDEAS

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    1. Yang, X. M. & Yang, X. Q. & Teo, K. L. & Hou, S. H., 2005. "Multiobjective second-order symmetric duality with F-convexity," European Journal of Operational Research, Elsevier, vol. 165(3), pages 585-591, September.
    2. Yang, X. M. & Yang, X. Q. & Teo, K. L. & Hou, S. H., 2005. "Second order symmetric duality in non-differentiable multiobjective programming with F-convexity," European Journal of Operational Research, Elsevier, vol. 164(2), pages 406-416, July.
    3. Mishra, S. K., 2000. "Multiobjective second order symmetric duality with cone constraints," European Journal of Operational Research, Elsevier, vol. 126(3), pages 675-682, November.
    4. S. K. Mishra & N. G. Rueda, 2006. "Second-Order Duality for Nondifferentiable Minimax Programming Involving Generalized Type I Functions," Journal of Optimization Theory and Applications, Springer, vol. 130(3), pages 479-488, September.
    5. I. Ahmad & Z. Husain, 2005. "Nondifferentiable Second-Order Symmetric Duality," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 22(01), pages 19-31.
    6. Christian Sommer, 2014. "Geometrical and Topological Properties of a Parameterized Binary Relation in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 815-840, December.
    7. Gulati, T.R. & Saini, Himani & Gupta, S.K., 2010. "Second-order multiobjective symmetric duality with cone constraints," European Journal of Operational Research, Elsevier, vol. 205(2), pages 247-252, September.
    8. Devi, G., 1998. "Symmetric duality for nonlinear programming problem involving [eta]-bonvex functions," European Journal of Operational Research, Elsevier, vol. 104(3), pages 615-621, February.
    9. Ahmad, I. & Husain, Z., 2010. "On multiobjective second order symmetric duality with cone constraints," European Journal of Operational Research, Elsevier, vol. 204(3), pages 402-409, August.
    10. Suneja, S. K. & Lalitha, C. S. & Khurana, Seema, 2003. "Second order symmetric duality in multiobjective programming," European Journal of Operational Research, Elsevier, vol. 144(3), pages 492-500, February.
    11. Yang, X. M. & Yang, X. Q. & Teo, K. L., 2003. "Non-differentiable second order symmetric duality in mathematical programming with F-convexity," European Journal of Operational Research, Elsevier, vol. 144(3), pages 554-559, February.
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