Augmented Lagrangian methods under the constant positive linear dependence constraint qualification. Andreani, R., Birgin, E. G., Martínez, J. M., & Schuverdt, M. L. *Mathematical Programming*, 111(1-2):5–32, June, 2007. Paper doi abstract bibtex Two Augmented Lagrangian algorithms for solving KKT systems are introduced. The algorithms differ in the way in which penalty parameters are updated. Possibly infeasible accumulation points are characterized. It is proved that feasible limit points that satisfy the Constant Positive Linear Dependence constraint qualiﬁcation are KKT solutions. Boundedness of the penalty parameters is proved under suitable assumptions. Numerical experiments are presented.

@article{andreani_augmented_2007,
title = {Augmented {Lagrangian} methods under the constant positive linear dependence constraint qualification},
volume = {111},
issn = {0025-5610, 1436-4646},
url = {http://link.springer.com/10.1007/s10107-006-0077-1},
doi = {10.1007/s10107-006-0077-1},
abstract = {Two Augmented Lagrangian algorithms for solving KKT systems are introduced. The algorithms differ in the way in which penalty parameters are updated. Possibly infeasible accumulation points are characterized. It is proved that feasible limit points that satisfy the Constant Positive Linear Dependence constraint qualiﬁcation are KKT solutions. Boundedness of the penalty parameters is proved under suitable assumptions. Numerical experiments are presented.},
language = {en},
number = {1-2},
urldate = {2023-10-09},
journal = {Mathematical Programming},
author = {Andreani, R. and Birgin, E. G. and Martínez, J. M. and Schuverdt, M. L.},
month = jun,
year = {2007},
pages = {5--32},
}

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