Andreani, R.; Birgin, E. G.; Martínez, J. M.; Schuverdt, M. L. On augmented Lagrangian methods with general lower-level constraints. (English) Zbl 1151.49027 SIAM J. Optim. 18, No. 4, 1286-1309 (2007). Summary: 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 \(3 \times 10^6\) variables and \( 14 \times 10^6\) constraints are solved in this way, using moderate computer time. All the codes are available at http://www.ime.usp.br/\(\sim\)egbirgin/tango/. Cited in 1 ReviewCited in 165 Documents MSC: 49M37 Numerical methods based on nonlinear programming 65F05 Direct numerical methods for linear systems and matrix inversion 65K05 Numerical mathematical programming methods 90C30 Nonlinear programming Keywords:nonlinear programming; augmented Lagrangian methods; global convergence; constraint qualifications; numerical experiments Software:Ipopt; SNOPT; GALAHAD; KELLEY; LANCELOT; CUTEr; ipfilter; ALGENCAN PDFBibTeX XMLCite \textit{R. Andreani} et al., SIAM J. Optim. 18, No. 4, 1286--1309 (2007; Zbl 1151.49027) Full Text: DOI Link