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A note on Fejér-monotone sequences in product spaces and its applications to the dual convergence of augmented Lagrangian methods

Maicon Marques Alves (maicon.alves***at***ufsc.br)
Benar Fux Svaiter (benar***at***impa.br)

Abstract: In a recent Math. Program. paper, Eckstein and Silva proposed a new error criterion for the approximate solutions of augmented Lagrangian subproblems. Based on a saddle-point formulation of the primal and dual problems, they proved that dual sequences generated by augmented Lagrangians under this error criterion are bounded and that theirs limit points are dual solutions. In this note, we prove a new result about the convergence of Fejér-monotone sequences in product spaces (which seems to be interesting by itself) and, as a consequence, we obtain the full convergence of the dual sequence generated by augmented Lagrangians under Eckstein and Silva's criterion.

Keywords: augmented Lagrangian, saddle-point problem, error criterion, Fejér-monotone sequences.

Category 1: Convex and Nonsmooth Optimization

Category 2: Nonlinear Optimization

Citation:

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Entry Submitted: 04/12/2014
Entry Accepted: 04/12/2014
Entry Last Modified: 04/14/2014

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