Mathematical Programming

, Volume 155, Issue 1–2, pp 613–616 | Cite as

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

  • M. Marques AlvesEmail author
  • B. F. Svaiter
Short Communication Series A


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 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.


Augmented Lagrangians Saddle-point problem Error criterion Fejér-monotone sequences 

Mathematics Subject Classification

90C25 90C30 


  1. 1.
    Eckstein, J., Silva, P.J.S.: A practical relative error criterion for augmented Lagrangians. Math. Program. 141(1–2, Ser. A), 319–348 (2013)zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2014

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade Federal de Santa CatarinaFlorianópolisBrazil
  2. 2.IMPARio de JaneiroBrazil

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