Improving ultimate convergence of an augmented Lagrangian method

Authors:
E. G. Birgin;J. M. Martínez
Affiliations:
Department of Computer Science, IME-USP, University of São Paulo, Rua do Matão, 1010 Cidade Universitária, São Paulo, SP, Brazil;Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, Campinas, SP, Brazil
Venue:
Optimization Methods & Software - Dedicated to Professor Michael J.D. Powell on the occasion of his 70th birthday
Year:
2008

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Abstract

Optimization methods that employ the classical Powell-Hestenes-Rockafellar augmented Lagrangian are useful tools for solving nonlinear programming problems. Their reputation decreased in the last 10 years due to the comparative success of interior-point Newtonian algorithms, which are asymptotically faster. In this research, a combination of both approaches is evaluated. The idea is to produce a competitive method, being more robust and efficient than its 'pure' counterparts for critical problems. Moreover, an additional hybrid algorithm is defined, in which the interior-point method is replaced by the Newtonian resolution of a Karush-Kuhn-Tucker (KKT) system identified by the augmented Lagrangian algorithm. The software used in this work is freely available through the Tango Project web page:http://www.ime.usp.br/∼egbirgin/tango/