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Minimization of some non-differentiable functionals by the Augmented Lagrangian Method of Hestenes and Powell (1975)

Fortin, Michel

Springer

Applied mathematics & optimization 2 (1975), S. 236-250

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ISSN: 1432-0606

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01464269

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