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

摘要

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-subdifferen-tial 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.