Augmented Lagrangian method with nonmonotone penalty parameters for constrained optimization

Autor(es)

Birgin, Ernesto G. ^[1] ; Martinez, J. M. ^[2]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS; v. 51, n. 3, p. 941-965, APR 2012.
• Citações Web of Science: 33

Resumo

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)

• Processo FAPESP: 06/03496-3 - Teoria e prática dos problemas de corte e empacotamento
• Beneficiário: Marcos Nereu Arenales
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 06/53768-0 - Métodos computacionais de otimização
• Beneficiário: José Mário Martinez Perez
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 09/10241-0 - Teoria e software em métodos computacionais de otimização
• Beneficiário: Ernesto Julián Goldberg Birgin
• Modalidade de apoio: Auxílio à Pesquisa - Regular