Robust Optimality Conditions And Duality For Uncertain Nonconvex Multiobjective Optimization Problems

In this paper,we study the optimality,duality and saddle point theorems for uncertain nonconvex multiobjective optimization problems by using the robust optimization method.First,based on Clarke subdifferential and robust necessary optimality conditions,a unified vector-valued dual model is proposed.The weak robust duality,strong robust duality and converse robust duality between the robust dual model and the robust counterpart of original problem are established under some suitable conditions.And the robust saddle point type sufficient and necessary optimality conditions for the problem are studied by generalized convexity.Secondly,the convexity,chain rule,Fermat’s theorem,Slater weak constraint specification and so on are generalized by using the upper semiregular convexificator.The KKT necessary optimality conditions and Fritz-John necessary optimality conditions of uncertain nonconvex multiobjective optimization problems are established respectively,and the sufficient optimality conditions are established by generalized pseudo-quasiconvexity.Finally,the mixed robust dual model of the problem is established,and the weak,strong and converse duality between the original problem and the dual problem are studied.The definition of saddle point is given and the saddle point theorem of the problem is characterized.