Journal of Optimization Theory and Applications

, Volume 147, Issue 1, pp 125–140 | Cite as

Duality and Exact Penalization for General Augmented Lagrangians

  • R. S. Burachik
  • A. N. Iusem
  • J. G. Melo


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.


Hausdorff topological spaces Nonsmooth optimization Nonconvex problem General augmented Lagrangian Duality Abstract convexity 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of South AustraliaAdelaideAustralia
  2. 2.Instituto de Matemática Pura e AplicadaRio de JaneiroBrazil

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