Structure of Efficient Sets for Strictly Quasi Convex Objectives

This paper studies the weak efficient set (WEff P) of a minimization problem P with k objectives defined on a convex set X of ℝⁿ. These objectives are continuous and belong to the class of so-called strictly quasiconvex functions, which contains, in particular, convex as well as linear fractional functions. When k is greater than n, it is of interest to replace the original problem by several subproblems, having at most n objectives. We show that if WEff P is bounded, the knowledge of the efficient sets of such subproblems, completely determines WEff P.