Global Optimization Approach to Optimizing Over the Efficient Set

We consider optimization problem over the efficient set of a linear vector problem where the objective function is a composite convex function of the criteria. We show that in this case the problem can be reduced to a single linear constrained convex maximization or a single convex-concave programming problem. The number of the “nonconvexity variables” in the both reduced forms is just equal to the number of the criteria. Some algoritmic aspects are discussed.