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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Super efficiency in vector optimization

Authors: J. M. Borwein and D. Zhuang
Journal: Trans. Amer. Math. Soc. 338 (1993), 105-122
MSC: Primary 90C29; Secondary 52A41
MathSciNet review: 1098432
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Abstract: We introduce a new concept of efficiency in vector optimization. This concept, super efficiency, is shown to have many desirable properties. In particular, we show that in reasonable settings the super efficient points of a set are norm-dense in the efficient frontier. We also provide a Chebyshev characterization of super efficient points for nonconvex sets and a scalarization theory when the underlying set is convex.

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Keywords: Vector optimization, efficiency, proper efficiency, super efficiency, Density Theorem, Chebyshev scalarization
Article copyright: © Copyright 1993 American Mathematical Society