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A new family of penalties for augmented Lagrangian methods
Author(s) -
Matioli L. C.,
Gonzaga C. C.
Publication year - 2008
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.596
Subject(s) - augmented lagrangian method , mathematics , iterated function , penalty method , logarithm , lagrangian , quadratic equation , regular polygon , convergence (economics) , dual (grammatical number) , function (biology) , mathematical optimization , mathematical analysis , geometry , art , literature , economics , economic growth , evolutionary biology , biology
We study a family of penalty functions for augmented Lagrangian methods, and concentrate on a penalty based on the modified logarithmic barrier function. The convex conjugate of this penalty induces a Bregman distance, and the dual iterates associated with the augmented Lagrangian algorithm correspond to the iterates produced by a proximal point algorithm based on this distance. The global convergence of the dual iterates is then proved. Moreover, the level curves of the quadratic approximation of the dual kernels associated with these penalty functions are the Dikin ellipsoids. Copyright © 2008 John Wiley & Sons, Ltd.