Renan W. Prado – Optimization Online

Primal-dual global convergence of an augmented Lagrangian method under the error bound condition

Published: 2025/07/22

Constrained Nonlinear Optimization, Nonlinear Optimization Augmented Lagrangian methods, constraint qualifications, Error bounds, local error bound, nonlinear programming

This work investigates global convergence properties of a safeguarded augmented Lagrangian method applied to nonlinear programming problems, with an emphasis on the role of constraint qualifications in ensuring boundedness of the Lagrange multiplier estimates, also known as dual sequences. When functions with locally Lipschitz continuous derivatives define the constraint set, we prove that the Error … Read more

Global convergence of a second-order augmented Lagrangian method under an error bound condition

Published: 2024/09/11, Updated: 2025/05/21

María Laura Schuverdt

Constrained Nonlinear Optimization, Nonlinear Optimization constant rank, constraint qualifications, local error bound, optimization methods, second-order conditions, sequential optimality conditions

This work deals with convergence to points satisfying the weak second-order necessary optimality conditions of a second-order safeguarded augmented Lagrangian method from the literature. To this end, we propose a new second-order sequential optimality condition that is, in a certain way, based on the iterates generated by the algorithm itself. This also allows us to … Read more