AKKT Optimality Conditions For Super Effcient Solution In Multiobjective Optimization

In this paper,we study optimality conditions for supper efficient solution to multiob-jective optimization problem.First,we give approximate Karush-Kuhn-Tucker(AKKT)optimality condition for convex multiobjective optimization problem with equality and inequality constraints by nonsmooth analytical tool—Clarke subdifferential.Then,we prove that AKKT optimality condition is necessary and sufficient for a point to be a su-per efficient solution when the sequences converge to zero.Next,we give the weak AKKT optimality condition that is proved to be a necessary condition for supper efficiency in nonconvex multiobjective optimization problem.Finally,we consider DC(difference of two convex multifunctions)set-valued optimization problem,and give sufficient condition for the existence of super efficient solution to DC set-valued optimization problem.