On relations of vector optimization results with C 1,1 data

In this article we prove that some of the sufficient and necessary optimality conditions obtained by Ginchev, Guerraggio, Luc [Appl. Math., 51, 5–36 (2006)] generalize (strictly) those presented by Guerraggio, Luc [J. Optim. Theory Appl., 109, 615–629 (2001)]. While the former paper shows examples for which the conditions given there are effective but the ones from the latter paper fail, it does not prove that generally the conditions it proposes are stronger. In the present note we complete this comparison with the lacking proof.