Abstract
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.
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Communicated by X.Q. Yang.
The authors are very grateful to the referees for their careful reading and correction of the previous version of the manuscript. In particular, the example in Remark 3.2 was motivated by an example provided by one of the referees. J.G. Melo was supported by CNPq-Brazil. J.G. Melo would like to thank the School of Mathematics and Statistics at the University of South Australia, for providing excellent conditions and a stimulating environment for carrying out his research.
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Burachik, R.S., Iusem, A.N. & Melo, J.G. Duality and Exact Penalization for General Augmented Lagrangians. J Optim Theory Appl 147, 125–140 (2010). https://doi.org/10.1007/s10957-010-9711-4
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DOI: https://doi.org/10.1007/s10957-010-9711-4