Weak stability and strong duality of a class of nonconvex infinite programs via augmented Lagrangian

In this paper we deal with weak stability and duality of a class of nonconvex infinite programs via augmented Lagrangian. Firstly, we study a concept of weak‐subdifferential of an extended real valued function on a topological linear space. Augmented Lagrangian functions and a concept of weak‐stability are constructed. Next, relations between weak‐stability and strong duality of problems via augmented Lagrangians are investigated. Applications for convex infinite programs are discussed. Saddle point theorems are established. An illustrative example is given.