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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Augmented Lagrangian method with nonmonotone penalty parameters for constrained optimization

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Author(s):
Birgin, Ernesto G. [1] ; Martinez, J. M. [2]
Total Authors: 2
Affiliation:
[1] Univ Sao Paulo, Inst Math & Stat, Dept Comp Sci, Sao Paulo - Brazil
[2] Univ Estadual Campinas, Dept Appl Math, Inst Math Stat & Sci Comp, Campinas, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS; v. 51, n. 3, p. 941-965, APR 2012.
Web of Science Citations: 33
Abstract

At each outer iteration of standard Augmented Lagrangian methods one tries to solve a box-constrained optimization problem with some prescribed tolerance. In the continuous world, using exact arithmetic, this subproblem is always solvable. Therefore, the possibility of finishing the subproblem resolution without satisfying the theoretical stopping conditions is not contemplated in usual convergence theories. However, in practice, one might not be able to solve the subproblem up to the required precision. This may be due to different reasons. One of them is that the presence of an excessively large penalty parameter could impair the performance of the box-constraint optimization solver. In this paper a practical strategy for decreasing the penalty parameter in situations like the one mentioned above is proposed. More generally, the different decisions that may be taken when, in practice, one is not able to solve the Augmented Lagrangian subproblem will be discussed. As a result, an improved Augmented Lagrangian method is presented, which takes into account numerical difficulties in a satisfactory way, preserving suitable convergence theory. Numerical experiments are presented involving all the CUTEr collection test problems. (AU)

FAPESP's process: 06/03496-3 - Theory and practice of cutting and packing problems
Grantee:Marcos Nereu Arenales
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 06/53768-0 - Computational methods of optimization
Grantee:José Mário Martinez Perez
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 09/10241-0 - Theory and software in computational methods for optimization
Grantee:Ernesto Julián Goldberg Birgin
Support Opportunities: Regular Research Grants