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The Structure of the Efficient Frontier of Finite-Dimensional Completely-Shaded Sets

✍ Scribed by Joël Benoist; Nicolae Popovici

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
141 KB
Volume
250
Category
Article
ISSN
0022-247X

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✦ Synopsis

The aim of this paper is to study the contractibility of the efficient frontier of closed free-disposal sets with respect to general ordering cones in the Euclidean space. In fact, it is shown that, under certain suitable continuity assumptions, the efficient frontier of a completely-shaded set is a strong deformation retract of its weakly-efficient frontier, the last one being homeomorphic to a hyperplane. In particular, for the standard positive cone, we can apply our result to multicriteria optimization to get the contractibility of the efficient outcome set.

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