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.
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Makarov, E.K., Rachkovski, N.N. Unified Representation of Proper Efficiency by Means of Dilating Cones. Journal of Optimization Theory and Applications 101, 141–165 (1999). https://doi.org/10.1023/A:1021775112119
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DOI: https://doi.org/10.1023/A:1021775112119