Optimality conditions with respect to an ordering map using an exact separation principle

In this note, we are concerned with a multiobjective optimization problem. Using a special (nonlinear) scalarization [1], together with an exact separation principle recently introduced by Zheng,Yang and Zou [11], we give necessary optimality conditions for locally weakly nondominated solutions with respect to a given ordering map. To get the results, a nonsmooth sequential Guignard constraint qualication is introduced.