Optimality Conditions And Duality Of A Class Of Robust Multiobjective Optimization Problem

Robust multiobjective optimization problem is an important direction in the research of multiobjective optimization theory and method.The research on optimality condition and duality theory is a classic research branch,which has been widely concerned by researchers.Some basic and significant results have been achieved.But most of the optimization problems in real life are nonconvex,the actual problems need to be satisfied,and many scholars have promoted the convexity to obtain a variety of generalization forms,among which the generalized pseudoconvex and strictly generalized pseudoconvex is an important generalized form.Therefore,this thesis focuses on a class of robust multiobjective optimization problems for nonsmooth and nonconvex real-valued functions,using the limit subdifferential of composite functions,and convexity generalization to generalized pseudounder and strictly generalized pseudoconvex,the optimal conditions for the robust Pareto(weak)efficient solution of multiobjective optimization problems can still be established.Further,two robust dual models of Wolfe type and Mond-Weir type are established and explored.Under generalized pseudounder and strictly generalized pseudoconvex,weak robust duality theory and strong robust duality theory for dual models of multiobjective problems are achieved.The first chapter is the introduction,the research background and significance of the multiobjective optimization problem,the main progress at home and abroad,the optimality condition of the robust multiobjective optimization problem and the research significance of the dual theory and the research status of related problems are introduced.This paper contains some preliminary knowledge,concepts and basic tools needed in the research work,as well as the definition of the relevant solutions and the definition of generalized convexity.The second chapter focuses on a class of robust multiobjective optimization problems for nonsmooth and nonconvex real-valued functions.The limit subdifferential of composite functions is obtained under the conditions of generalized pseudounder and strictly generalized pseudoconvex.Optimality sufficient conditions for robust multiobjective optimization problems are explored.The third chapter focuses on this kind of robust multiobjective optimization problem,and establishes two classical robust dual models of Wolfe type and Mond-Weir type.Using the normal cone and the limit subdifferential and under the condition of generalized pseudoconvex and strictly generalized pseudoconvex,the weak robust dual theory and strong robust duality theory between the initial problem and the dual problem are explored.