Unified Representation of Proper Efficiency by Means of Dilating Cones

E. K. Makarov and N. N. Rachkovski
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E. K. Makarov: Academy of Sciences of Belarus
N. N. Rachkovski: Academy of Sciences of Belarus

Journal of Optimization Theory and Applications, 1999, vol. 101, issue 1, No 8, 165 pages

Abstract: 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.

Keywords: Vector optimization; Borwein proper efficiency; Hartley proper efficiency; Henig proper efficiency; superefficiency (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1023/A:1021775112119

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