The structure of the efficient frontier of finite-dimensional completely-shaded sets

[摘要] 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. ln particular, for the standard positive cone, we can apply our result to multicriteria optimization to get the contractibility of the efficient outcome set, (C) 2000 Academic Press.

[发布日期] 2000-10-01

[关键词] vector optimization;efficiency;shaded sets;retracts;contractibility