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

The aim of this paper is to study the contractibility of the efficient fron tier of closed free-disposal sets with respect to general ordering cones in the Euclidean space. In fact, it is shown that, under certain suitable con tinuity 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 positiv e cone, we can apply our result to multicriteria optimization to get the co ntractibility of the efficient outcome set, (C) 2000 Academic Press.