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

Andrea Cristofari; Gianni Di Pillo; Giampaolo Liuzzi; Stefano Lucidi

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arXiv · 2104.15018

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

Andrea Cristofari·Gianni Di Pillo·Giampaolo Liuzzi·Stefano Lucidi

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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.

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BibTeX RIS

Andrea Cristofari, Gianni Di Pillo, Giampaolo Liuzzi, Stefano Lucidi. 2021-04-30. An augmented Lagrangian method exploiting an active-set strategy and second-order information. https://arxiv.org/abs/2104.15018

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