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Augmented Lagrangians quadratic growth and second-order sufficient optimality conditions
(Taylor & Francis Ltd, 2020-08-21)
It is well-known that the primal quadratic growth condition of the classical augmented Lagrangian around a local minimizer can be obtained under the second-order sufficient optimality condition. In this paper, we show that ...
Augmented Lagrangians quadratic growth and second-order sufficient optimality conditions
(Taylor & Francis Ltd, 2020-08-21)
It is well-known that the primal quadratic growth condition of the classical augmented Lagrangian around a local minimizer can be obtained under the second-order sufficient optimality condition. In this paper, we show that ...
On the cost of solving augmented Lagrangian subproblems
(Springer, 2020-07)
At each iteration of the augmented Lagrangian algorithm, a nonlinear subproblem is being solved. The number of inner iterations (of some/any method) needed to obtain a solution of the subproblem, or even a suitable approximate ...
A second-order convergence augmented Lagrangian method using non-quadratic penalty functions
(Springer, 2019-06)
The purpose of the present paper is to study the global convergence of a practical Augmented Lagrangian model algorithm that considers non-quadratic Penalty–Lagrangian functions. We analyze the convergence of the model ...
An augmented lagrangian method to solve three-dimensional nonlinear contact problems
(Planta Piloto de Ingeniería Química, 2012-11)
A finite element formulation to deal with the friction contact problem between an elastic body and a rigid foundation is presented. An augmented Lagrangian method, which incorporates two Lagrange multipliers and a slack ...
The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems
(Taylor & Francis Ltd, 2012-12)
Augmented Lagrangian methods are effective tools for solving large-scale nonlinear programming problems. At each outer iteration, a minimization subproblem with simple constraints, whose objective function depends on updated ...
A regularization method based on level sets and augmented Lagrangian for parameter identification problems with piecewise constant solutions
(IOP Publishing, 2018-10-01)
We propose and analyse a regularization method for parameter identification problems modeled by ill-posed nonlinear operator equations, where the parameter to be identified is a piecewise constant function taking known ...
Meso-scale fracture simulation using an augmented Lagrangian approach
(Sage Publications Ltd, 2016-08)
A cohesive zone model implemented in an augmented Lagrangian functional is used for simulation of meso-scale fracture problems in this paper. The method originally developed by Lorentz is first presented in a rigorous ...
A Path-following technique implemented in a Lagrangian formulation to model quasi-brittle fracture
(Pergamon-Elsevier Science Ltd, 2018-03)
A path-following strategy based on an energy release criterion is proposed and implemented in an augmented Lagrangian formulation to model localized cohesive cracks. The model is formulated in a rigourous variational ...
A Sequential Optimality Condition Related to the Quasi-normality Constraint Qualification and Its Algorithmic Consequences
(Society for Industrial and Applied Mathematics, 2019-03)
In the present paper, we prove that the augmented Lagrangian method converges to KKT pointsunder the quasinormality constraint qualification, which is associated with the external penalty theory. An interesting consequence ...