In this paper, we introduce generalized augmented Lagrangian by relaxing the convexity assumption on the usual augmenting function. Applications are given to establish strong duality and exact penalty representation for the problem of minizing an extended real valued function. More specifically, a strong duality result based on the generalized augmented Lagrangian is established, and a necessary and sufficient condition for the exact penalty representation in the framework of generalized augmented Lagrangian is obtained.
- Extended real-valued function
- Generalized augmented Lagrangian
- Exact penalty representation