中文摘要：

作者介绍了一种基于向量值延拓函数的广义增广拉格朗日函数,建立了基于广义增广拉格朗日函数的集值广义增广拉格朗日对偶映射和相应的对偶问题,得到了相应的强对偶和弱对偶结果,将所获结果应用到约束向量优化问题.该文的结果推广了一些已有的结论.

英文摘要：

In this paper, the author introduces a generalized augmented Lagrangian for minimizing an extended vector-valued function. Based on the generalized augmented Lagrangian, the author constructs set-valued dual functions and dual optimization problems, obtain weak and strong duality results without any convexity required, apply the results for solving a constrained vector optimization problem. The results improve and generalize some known results.