On the Structure of the Weakly Efficient Set for Quasiconvex Vector Minimization

We investigate conditions under which the weakly efficient set for minimization of m objective functions on a closed and convex X⊂ R d (m> d) is fully determined by the weakly efficient sets for all n-objective subsets for some n< m. For quasiconvex functions, it is their union with n= d+ 1. For lower semi-continuous explicitly quasiconvex functions, the weakly efficient set equals the linear enclosure of their union with n= d, as soon as it is bounded. Sufficient conditions for the weakly efficient set to be bounded or unbounded are also investigated.