On Augmented Lagrangian Methods with General Lower-Level Constraints

Abstract

Abstract. 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 param-eters are discussed. The reliability of the approach is tested by means of a comparison against Ipopt and Lancelot B. 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 × 106 vari-ables and 14 × 106 constraints are solved in this way, using moderate computer time. The codes are free for download in www.ime.usp.br/∼egbirgin/tango/