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

Authors:
Gianni Pillo;Giampaolo Liuzzi;Stefano Lucidi;Laura Palagi
Affiliations:
Dipartimento di Informatica e Sistemistica "Antonio Ruberti", Università di Roma "La Sapienza", Roma, Italy 00185;CNR---Consiglio Nazionale delle Ricerche, IASI---Istituto di Analisi dei Sistemi ed Informatica "A. Ruberti", Roma, Italy 00185;Dipartimento di Informatica e Sistemistica "Antonio Ruberti", Università di Roma "La Sapienza", Roma, Italy 00185;Dipartimento di Informatica e Sistemistica "Antonio Ruberti", Università di Roma "La Sapienza", Roma, Italy 00185
Venue:
Computational Optimization and Applications
Year:
2010

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Abstract

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.