Duality and Exact Penalization for General Augmented Lagrangians
We consider a problem of minimizing an extended real-valued function defined in a Hausdorff topological space. We study the dual problem induced by a general augmented Lagrangian function. Under a simple set of assumptions on this general augmented Lagrangian function, we obtain strong duality and existence of exact penalty parameter via an abstract convexity approach. We show that every cluster point of a sub-optimal path related to the dual problem is a primal solution. Our assumptions are more general than those recently considered in the related literature.
KeywordsHausdorff topological spaces Nonsmooth optimization Nonconvex problem General augmented Lagrangian Duality Abstract convexity
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