On the Global Convergence of a General Class of Augmented Lagrangian Methods

Ernesto G. Birgin (), Gabriel Haeser (), Nelson Maculan () and Lennin Mallma Ramirez ()
Additional contact information
Ernesto G. Birgin: University of São Paulo
Gabriel Haeser: University of São Paulo
Nelson Maculan: Federal University of Rio de Janeiro
Lennin Mallma Ramirez: Federal University of Rio de Janeiro

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 3, No 1, 25 pages

Abstract: Abstract In [E. G. Birgin, R. Castillo and J. M. Martínez, Computational Optimization and Applications 31, pp. 31–55, 2005], a general class of safeguarded augmented Lagrangian methods is introduced which includes a large number of different methods from the literature. Besides a numerical comparison including 65 different methods, primal-dual global convergence to a KKT point is shown under a (strong) regularity condition. In the present work, we generalize this framework by considering also classical/non-safeguarded Lagrange multipliers updates. This is done in order to give a rigorous theoretical study to the so-called hyperbolic augmented Lagrangian method, which is not safeguarded, while also including the classical Powell-Hestenes-Rockafellar augmented Lagrangian method. Our results are based on a weak regularity condition which does not require boundedness of the set of Lagrange multipliers. Somewhat surprisingly, in non-safeguarded methods, we show that the penalty parameter may be kept constant at every iteration even in the lack of convexity assumptions. Numerical experiments with all the problems in the Netlib and CUTEst collections are reported to compare and discuss the different approaches.

Keywords: Nonlinear optimization; Augmented Lagrangian methods; Convergence; Numerical experiments; 90C30; 65K05 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-025-02734-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:206:y:2025:i:3:d:10.1007_s10957-025-02734-0

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-025-02734-0

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().