An equivalent one level optimization problem to a semivectorial bilevel problem

In this paper, we are concerned with a bilevel optimization problem (P_{0}), where the lower level problem is a vector optimization problem. First, we give an equivalent one level optimization problem for which the nonsmooth Mangasarian–Fromowitz constraint qualification can hold at feasible solution. Using a special scalarization function, one deduces necessary optimality condition for the initial problem.