On the convexity and cardinality of the efficient set in multicriteria programming

The literature on the Multiple Criteria Optimization shows that it is quite difficult to deal with in extenso the efficient points set E[X] of X ⊂ ℝⁿ. For this reason, our contribution will be focused on the localization of the set E[X] under its geometrical aspect. In this paper, we focus our efforts on the convexity and the cardinality of E[X]. Some cones and the separation theory of convex sets have an important role to locate E[X]. The condition for E[X] to be convex and to be reduced to one point (‘singleton’) is established. Linear subroutines followed by a summary-diagram conclude our note.