| Full text | |
| Author(s): |
Birgin, Ernesto G.
;
Haeser, Gabriel
;
Maculan, Nelson
;
Ramirez, Lennin Mallma
Total Authors: 4
|
| Document type: | Journal article |
| Source: | JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS; v. 206, n. 3, p. 25-pg., 2025-09-01. |
| Abstract | |
In [E. G. Birgin, R. Castillo and J. M. Mart & iacute;nez, 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. (AU) | |
| FAPESP's process: | 22/16733-6 - Reconstruction of Voronoi diagrams in electrical impedance tomography |
| Grantee: | Danilo Rodrigues de Souza |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 22/05803-3 - Cutting, packing, lot-sizing, scheduling, routing and location problems and their integration in industrial and logistics settings |
| Grantee: | Reinaldo Morabito Neto |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry |
| Grantee: | Francisco Louzada Neto |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |
| FAPESP's process: | 23/08706-1 - Numerical optimization |
| Grantee: | Ernesto Julián Goldberg Birgin |
| Support Opportunities: | Research Projects - Thematic Grants |