Stationary Condition for Borwein Proper Efficient Solutions of Nonsmooth Multiobjective Problems with Vanishing Constraints

This paper discusses optimality conditions for Borwein proper efficient solutions of nonsmooth multiobjective optimization problems with vanishing constraints. A new notion in terms contingent cone and upper directional derivative is introduced, a necessary condition the solution considered problem derived. The concept ε Abadie data qualification also which called strictly strong stationary obtained. In view condition, convexity objective functions, quasi-convexity constrained sufficient are presented. Some examples given to illustrate reasonability obtained results.