Duality on approximate solutions of nonconvex vector optimization problems

In this paper, we focus on nonconvex vector optimization problems. By employing nonlinear scalarization techniques, we introduce a real-valued augmented Lagrangian function and construct the augmented Lagrangian dual optimization 问题. We derive weak, strong, and converse duality theorems for approximately weakly efficient solutions of the vector optimization problems. Furthermore, under suitable 条件, corresponding duality results for approximately Benson-properly efficient solutions are also presented. The relationships between approximately weakly (Benson-properly) efficient solutions and the approximate saddle points of the augmented Lagrangian function are discussed. The results obtained in this paper do not require any convexity 条件, which enables us to more effectively handle nonconvex vector optimization problems.