Weighting factor results in vector optimization

This paper deals with the study, in a convex vector optimization problem, of the set of efficient solutions and the set of properly efficient solutions, the latter being obtained by a weighting factor technique. Relationships between these two sets are discussed; they are shown to be nonempty when the objective functions have no common direction of recession and to be closed and equal when, moreover, the objective functions are locally polyhedral. An example is provided where the set of efficient solutions is not included in the closure of the nonempty set of properly efficient solutions.The author wishes to thank the unknown referee for the helpful comments that improved the quality of this paper.