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.

Cristofari, A., Di Pillo, G., Liuzzi, G., Lucidi, S. (2022). An Augmented Lagrangian Method Exploiting an Active-Set Strategy and Second-Order Information. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS(193), 300-323 [10.1007/s10957-022-02003-4].

An Augmented Lagrangian Method Exploiting an Active-Set Strategy and Second-Order Information

Cristofari A.
;
2022-01-01

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.
2022
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/09 - RICERCA OPERATIVA
English
Augmented Lagrangian methods
Constrained optimization
Large-scale optimization
Nonlinear programming algorithms
Cristofari, A., Di Pillo, G., Liuzzi, G., Lucidi, S. (2022). An Augmented Lagrangian Method Exploiting an Active-Set Strategy and Second-Order Information. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS(193), 300-323 [10.1007/s10957-022-02003-4].
Cristofari, A; Di Pillo, G; Liuzzi, G; Lucidi, S
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/312685
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