A note on Fejer-monotone sequences in product spaces and its applications to the dual convergence of augmented Lagrangian methods
成果类型：
Article
署名作者：
Alves, M. Marques; Svaiter, B. F.
署名单位：
Universidade Federal de Santa Catarina (UFSC); Instituto Nacional de Matematica Pura e Aplicada (IMPA)
刊物名称：
MATHEMATICAL PROGRAMMING
ISSN/ISSBN：
0025-5610
DOI：
10.1007/s10107-014-0849-y
发表日期：
2016
页码：
613-616
关键词：
摘要：
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 their limit points are dual solutions. In this note, we prove a new result about the convergence of Fej,r-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.