Abstract

In the paper “Contractibility of the efficient set in strictly quasiconcave vector maximization” [J. Optimization Theory Appl. 110, No. 2, 325–336 (2001; Zbl 1009.90101)], \textit{J. Benoist} stated the conjecture saying that the efficient solution set of any semistrictly quasiconcave vector maximization problem on a nonempty compact convex feasible domain is contractible. This paper presents some remarks on that conjecture. In particular, we propose an example of a linear fractional vector optimization problem on a (noncompact) polyhedral convex feasible domain whose solution set is arcwise connected, but not contractible. This example shows that connected components of the efficient solution set of a semistrictly quasiconcave vector maximization problem on a noncompact convex feasible domain are not necessarily contractible.