Second‐order asymptotic differential properties and optimality conditions for weak vector variational inequalities

In this paper, by virtue of an asymptotic second‐order contingent derivative and an asymptotic second‐order Φ‐contingent cone, differential properties of a class of set‐valued maps are investigated and an explicit expression of their asymptotic second‐order contingent derivatives is established. Then, second‐order necessary optimality conditions of solutions are obtained for weak vector variational inequalities.