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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 ...
A mortar method combined with an augmented Lagrangian approach for treatment of mechanical contact problems
(Springer, 2014)
This work presents a mixed penalty-duality formulation from an augmented Lagrangian approach for treating the contact inequality constraints. The augmented Lagrangian approach allows to regularize the non differentiable ...
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 ...