Continuity properties of solutions of vector optimization

Abstract: This paper characterizes upper semicontinuity and lower semicontinuity of weakly efficient solution mapping and efficient solution mapping S on the space of continuous -dimension-vector-real-valued objective functions on a nonempty compact set X. As applications, some more interesting results about the properties of weakly efficient solutions and efficient solutions are obtained, such as the upper semicontinuity of S at f in implies the closedness and connectedness of the set of efficient solutions, any essential weakly efficient solution of f can be approximated by a sequence of efficient solutions of f (i.e., ), and in the sense of Baire categories “most” of vector optimization problems in for efficient solutions are essential, and so on. [Copyright &y& Elsevier]