Augmented Lagrangians with possible infeasibility and finite termination for global nonlinear programming

Autor(es)

Birgin, E. G. ^[1] ; Martinez, J. M. ^[2] ; Prudente, L. F. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Dept Comp Sci, Inst Math & Stat, Sao Paulo - Brazil

^[2] Univ Estadual Campinas, Dept Appl Math, Inst Math Stat & Sci Comp, Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Global Optimization; v. 58, n. 2, p. 207-242, FEB 2014.
• Citações Web of Science: 9

Resumo

In a recent paper, Birgin, Floudas and Martinez introduced an augmented Lagrangian method for global optimization. In their approach, augmented Lagrangian subproblems are solved using the BB method and convergence to global minimizers was obtained assuming feasibility of the original problem. In the present research, the algorithm mentioned above will be improved in several crucial aspects. On the one hand, feasibility of the problem will not be required. Possible infeasibility will be detected in finite time by the new algorithms and optimal infeasibility results will be proved. On the other hand, finite termination results that guarantee optimality and/or feasibility up to any required precision will be provided. An adaptive modification in which subproblem tolerances depend on current feasibility and complementarity will also be given. The adaptive algorithm allows the augmented Lagrangian subproblems to be solved without requiring unnecessary potentially high precisions in the intermediate steps of the method, which improves the overall efficiency. Experiments showing how the new algorithms and results are related to practical computations will be given. (AU)

• Processo FAPESP: 10/10133-0 - Problemas de corte, empacotamento, dimensionamento de lotes e programação da produção, e suas integrações em contextos industriais e logísticos
• Beneficiário: Reinaldo Morabito Neto
• 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