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Unified Representation of Proper Efficiency by Means of Dilating Cones

Author

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  • E. K. Makarov

    (Academy of Sciences of Belarus)

  • N. N. Rachkovski

    (Academy of Sciences of Belarus)

Abstract

We reduce the definitions of proper efficiency due to Hartley, Henig, Borwein, and Zhuang to a unified form based on the notion of a dilating cone, i.e., an open cone containing the ordering cone. This new form enables us to obtain a comprehensive comparison among these and other kinds of proper efficiency. The most advanced results are obtained for a special class of proper efficiencies corresponding to one-parameter families of uniform dilations. This class is sufficiently wide and includes, for example, the Hartley and Henig proper efficiencies as well as superefficiency.

Suggested Citation

  • E. K. Makarov & N. N. Rachkovski, 1999. "Unified Representation of Proper Efficiency by Means of Dilating Cones," Journal of Optimization Theory and Applications, Springer, vol. 101(1), pages 141-165, April.
    • Handle: RePEc:spr:joptap:v:101:y:1999:i:1:d:10.1023_a:1021775112119
    DOI: 10.1023/A:1021775112119
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    References listed on IDEAS

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    1. X. Y. Zheng, 1997. "Proper Efficiency in Locally Convex Topological Vector Spaces," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 469-486, August.
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    Cited by:

    1. Nguyen Hoang Anh & Phan Khanh, 2014. "Higher-order optimality conditions for proper efficiency in nonsmooth vector optimization using radial sets and radial derivatives," Journal of Global Optimization, Springer, vol. 58(4), pages 693-709, April.
    2. H. T. H. Diem & P. Q. Khanh & L. T. Tung, 2014. "On Higher-Order Sensitivity Analysis in Nonsmooth Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 463-488, August.
    3. Nguyen Xuan Duy Bao & Phan Quoc Khanh & Nguyen Minh Tung, 2022. "Quasi-contingent derivatives and studies of higher-orders in nonsmooth optimization," Journal of Global Optimization, Springer, vol. 84(1), pages 205-228, September.
    4. Fernando García-Castaño & Miguel Ángel Melguizo-Padial & G. Parzanese, 2023. "Sublinear scalarizations for proper and approximate proper efficient points in nonconvex vector optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(3), pages 367-382, June.

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