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

Andrea Cristofari (), Gianni Di Pillo (), Giampaolo Liuzzi () and Stefano Lucidi ()
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Andrea Cristofari: University of Padua
Gianni Di Pillo: Sapienza University of Rome
Giampaolo Liuzzi: Sapienza University of Rome
Stefano Lucidi: Sapienza University of Rome

Journal of Optimization Theory and Applications, 2022, vol. 193, issue 1, No 15, 300-323

Abstract: 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.

Keywords: Constrained optimization; Augmented Lagrangian methods; Nonlinear programming algorithms; Large-scale optimization; 90C30; 65K05 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-022-02003-4

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