A truncated Newton method in an augmented Lagrangian framework for nonlinear programming

In this paper we propose a primal-dual algorithm for the solution of general nonlinear programming problems. The core of the method is a local algorithm which relies on a truncated procedure for the computation of a search direction, and is thus suitable for large scale problems. The truncated direc...

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Veröffentlicht in:Computational optimization and applications Jg. 45; H. 2; S. 311 - 352
Hauptverfasser: Di Pillo, Gianni, Liuzzi, Giampaolo, Lucidi, Stefano, Palagi, Laura
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Boston Springer US 01.03.2010
Springer Nature B.V
Schlagworte:
Algorithms
Convex and Discrete Geometry
Globalization
Lagrange multiplier
Management Science
Mathematics
Mathematics and Statistics
Nonlinear programming
Operations Research
Operations Research/Decision Theory
Optimization
Optimization techniques
Statistics
Studies
Large scale optimization
Exact augmented Lagrangian functions
Truncated Newton-type algorithms
Nonlinear programming algorithms
Constrained optimization
ISSN:0926-6003, 1573-2894
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Zusammenfassung:In this paper we propose a primal-dual algorithm for the solution of general nonlinear programming problems. The core of the method is a local algorithm which relies on a truncated procedure for the computation of a search direction, and is thus suitable for large scale problems. The truncated direction produces a sequence of points which locally converges to a KKT pair with superlinear convergence rate. The local algorithm is globalized by means of a suitable merit function which is able to measure and to enforce progress of the iterates towards a KKT pair, without deteriorating the local efficiency. In particular, we adopt the exact augmented Lagrangian function introduced in Pillo and Lucidi (SIAM J. Optim. 12:376–406, 2001 ), which allows us to guarantee the boundedness of the sequence produced by the algorithm and which has strong connections with the above mentioned truncated direction. The resulting overall algorithm is globally and superlinearly convergent under mild assumptions.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-008-9216-3