The optimization literature is vast in papers dealing with improvements on the global
convergence of augmented Lagrangian schemes. Usually, the results are based on weak …

Global convergence of augmented Lagrangian methods to a first-order stationary point is
well-known to hold under considerably weak constraint qualifications. In particular, several …

This paper discusses the use of a stopping criterion based on the scaling of the Karush–
Kuhn–Tucker (KKT) conditions by the norm of the approximate Lagrange multiplier in the …

Augmented Lagrangian methods with convergence to second-order stationary points in
which any constraint can be penalized or carried out to the subproblems are considered in …

Algencan is a well established safeguarded Augmented Lagrangian algorithm introduced in
[R. Andreani, EG Birgin, JM Martínez, and ML Schuverdt, On Augmented Lagrangian …

We establish local convergence and rate of convergence of the classical augmented
Lagrangian algorithm under the sole assumption that the dual starting point is close to a …

We consider the global convergence properties of a class of augmented Lagrangian
methods for solving nonlinear programming problems. In the proposed method, linear …

In the past several years, augmented Lagrangian methods have been successfully applied
to several classes of nonconvex optimization problems, inspiring new developments in both …

At each iteration of the safeguarded augmented Lagrangian algorithm Algencan, a bound-
constrained subproblem consisting of the minimization of the Powell–Hestenes–Rockafellar …

Augmented Lagrangian (AL) algorithms are very popular and successful methods for solving
constrained optimization problems. Recently, global convergence analysis of these methods …