Optimality Conditions And Duality Of Approximate Robust Solutions For Uncertain Multiobjective Optimization Problems

Multi-objective decision analysis is an important method to solve economic and management problems.In this paper,a robust method is used to study the multi-objective problems with uncertain data under objective function and constraint function.By introducing a new constraint specification,it can be viewed as an extension of an existing constraint specification.The Karush-Kuhn-Tucker type necessary conditions for optimality of robust -quasi(weakly)efficient solutions are obtained by using the Mordukhovich subderivatives and Clarke subderivatives.Under the(strictly)pseudo-quasi generalized convexity hypothesis,the Optimality sufficient conditions for robust approximate critical points of(UMP)to be robust -quasi(weakly)efficient solutions are given.On this basis,a vector-valued Lagrangian function for multi-objective optimization problems is proposed,and a unified vector-valued optimistic dual model is proposed by using the vector-valued Lagrangian function.Under the generalized convex hypothesis,the weak/strong and inverse robust duality between the duality problem and(UMP)are established.