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On Augmented Lagrangian methods with general lower-level constraints
 

Summary: On Augmented Lagrangian methods with general lower-level
constraints
R. Andreani
E. G. Birgin
J. M. Mart´inez
M. L. Schuverdt §
March 3, 2005
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 where the constraints are only of the lower-level type. Two methods of this
class are introduced and analyzed. Inexact resolution of the lower-level constrained sub-
problems is considered. Global convergence is proved using the Constant Positive Linear
Dependence constraint qualification. Conditions for boundedness of the penalty parameters
are discussed. The reliability of the approach is tested by means of an exhaustive comparison
against Lancelot . All the problems of the Cute collection are used in this comparison.
Moreover, 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 solv-
ing the subproblems. Problems of this type with more than 3 × 106
variables and 14 × 106

  

Source: Andreani, Roberto - Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas

 

Collections: Mathematics