An augmented Lagrangian method exploiting an active-set strategy and second-order information

TL;DR

This paper introduces a modified augmented Lagrangian method that incorporates second-order information and an active-set strategy, achieving faster convergence and improved robustness for nonlinear optimization problems with constraints.

Contribution

The paper presents a novel modification of ALGENCAN that integrates second-order information and active-set strategies, maintaining convergence properties and enhancing robustness.

Findings

Algorithm has the same convergence as ALGENCAN.

Achieves asymptotic quadratic convergence rate.

Numerical results show increased robustness.

Abstract

In this paper, we consider nonlinear optimization problems with nonlinear equality constraints and bound constraints on the variables. For the solution of such problems, many augmented Lagrangian methods have been defined in the literature. Here, we propose to modify one of these algorithms, namely ALGENCAN by Andreani et al., in such a way to incorporate second-order information into the augmented Lagrangian framework, using an active-set strategy. We show that the overall algorithm has the same convergence properties as ALGENCAN and an asymptotic quadratic convergence rate under suitable assumptions. The numerical results confirm that the proposed algorithm is a viable alternative to ALGENCAN with greater robustness.