Abstract
The Augmented Lagrangian Method of Hestenes and Powell is presented here in a more general case, including Fenchel's duality, using some recent results of R. T. Rockafellar which are here extended. It is shown that for some functionals which contain a non-differentiable term which is the support function of a convex set, the Augmented Lagrangian Method provides a natural way to marry standard duality techniques and regularisation techniques. An application to visco-plastic flows is presented and numerical results are given. A convergence proof is given for the algorithm used. Another application to elasto-plastic torsion is also signaled.
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Communicated by A. Bensoussan
This work was partly supported by a FCAC grant from the Department of Education of the Province of Quebec, Canada.
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Fortin, M. Minimization of some non-differentiable functionals by the Augmented Lagrangian Method of Hestenes and Powell. Appl Math Optim 2, 236–250 (1975). https://doi.org/10.1007/BF01464269
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DOI: https://doi.org/10.1007/BF01464269