A new family of penalties for augmented Lagrangian methods

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.

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