ON AUGMENTED LAGRANGIAN METHODS WITH GENERAL LOWER-LEVEL CONSTRAINTS

Autor(es)

Andreani, R. ^[1] ; Birgin, E. G. ^[2] ; Martinez, J. M. ^[1] ; Schuverdt, M. L. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Dept Appl Math, IMECC, BR-13081970 Campinas, SP - Brazil

^[2] Univ Sao Paulo, Dept Comp Sci IME, BR-05508090 Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: SIAM JOURNAL ON OPTIMIZATION; v. 18, n. 4, p. 1286-1309, 2007.
• Citações Web of Science: 166

Resumo

Augmented Lagrangian methods with general lower-level constraints are considered in the present research. These methods are useful when efficient algorithms exist for solving subproblems in which the constraints are only of the lower-level type. Inexact resolution of the lower-level constrained subproblems is considered. Global convergence is proved using the constant positive linear dependence constraint qualification. Conditions for boundedness of the penalty parameters are discussed. The resolution of location problems in which many constraints of the lower-level set are nonlinear is addressed, employing the spectral projected gradient method for solving the subproblems. Problems of this type with more than 3 x 10(6) variables and 14 x 10(6) constraints are solved in this way, using moderate computer time. All the codes are available at http://www.ime.usp.br/similar to egbirgin/tango/. (AU)

• Processo FAPESP: 01/04597-4 - Métodos computacionais de otimização
• Beneficiário: José Mário Martinez Perez
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 03/09169-6 - Desenvolvimento e aplicacao de metodos numericos para otimizacao continua de grande porte.
• Beneficiário: Ernesto Julián Goldberg Birgin
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 02/00832-1 - Problemas e métodos em programação não linear
• Beneficiário: María Laura Schuverdt
• Modalidade de apoio: Bolsas no Brasil - Doutorado Direto