Contractibility of the Efficient Set in Strictly Quasiconcave Vector Maximization

摘要

In this paper, we investigate the contractibility of the efficient frontier in a vector maximization problem defined by a continuous vector-valued strictly quasiconcave function g = (g_1, …, g_n) and a convex compact set D in R~p. It is shown that the efficient frontier is contractible if one of the components of g is strongly quasiconcave on X. This work extends a result by Sun (see Ref. 1), which confirms the connectedness of the efficient frontier.