Separations And Optimality Of Constrained Multiobjective Optimization Via Improvement Sets

In this thesis,we use image space analysis method to investigate the separations and optimality conditions for the optimal solution defined by the improvement set of a constrained multiobjective optimization problem.We firstly introduce two separation functions of constrained multiobjective optimization problem: a vector-valued regular weak separation function and a scalar weak separation function via a nonlinear scalarization function defined in terms of an improvement set.Secondly,saddle-point type optimality sufficient conditions for the optimal solution of the multiobjective optimization problem are established respectively by the vector-valued regular weak separation function and a scalar weak separation function.Next,we also obtain the relationships between the optimal solution and approximate efficient solution of the multiobjective optimization problem.Finally,saddle-point type optimality necessary conditions for the optimal solution of the multiobjective optimization problem are established respectively by the(regular)linear separation between the approximate image of the multiobjective optimization problem and a closed convex cone.