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Summary: Augmented Lagrangian methods under the Constant Positive
Linear Dependence constraint qualification
R. Andreani
E. G. Birgin
J. M. Mart´inez
M. L. Schuverdt §
September 14, 2005.
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. Bounded-
ness of the penalty parameters is proved under suitable assumptions. Numerical experiments
are presented.
Key words: Nonlinear programming, Augmented Lagrangian methods, KKT systems, nu-
merical experiments.
1 Introduction
Let F : IRn IRn, D IRn. The Variational Inequality Problem (VIP) defined by (F, D) (see,
for example, [34]) consists of finding x D such that F(x)T d 0 for all d in the tangent cone
TD(x) ([3], page 334) .
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