Dominators for multiple-objective quasiconvex maximization problems

In this paper we address the problem of finding a dominator for a multiple- objective maximization problem with quasiconvex functions. The one-dimensio nal case is discussed in some detail, showing how a Branch-and-Bound proced ure leads to a dominator with certain minimality properties. Then, the well -known result stating that the set of vertices of a polytope S contains an optimal solution for single-objective quasiconvex maximization problems is extended to multiple-objective problems, showing that, under upper-semicont inuity assumptions, the set of (k - 1)-dimensional faces is a dominator for k-objective problems. In particular, for biobjective quasiconvex problems on a polytope S, the edges of S constitute a dominator, from which a domina tor with minimality properties can be extracted by Branch-and Bound methods .