Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization

Authors:
E. G. Birgin;J. M. Martínez
Affiliations:
Department of Computer Science IME-USP, University of São Paulo, São Paulo, Brazil 05508-090;Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, Campinas, Brazil 13081-970
Venue:
Computational Optimization and Applications
Year:
2008

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Abstract

Augmented Lagrangian methods for large-scale optimization usually require efficient algorithms for minimization with box constraints. On the other hand, active-set box-constraint methods employ unconstrained optimization algorithms for minimization inside the faces of the box. Several approaches may be employed for computing internal search directions in the large-scale case. In this paper a minimal-memory quasi-Newton approach with secant preconditioners is proposed, taking into account the structure of Augmented Lagrangians that come from the popular Powell---Hestenes---Rockafellar scheme. A combined algorithm, that uses the quasi-Newton formula or a truncated-Newton procedure, depending on the presence of active constraints in the penalty-Lagrangian function, is also suggested. Numerical experiments using the Cute collection are presented.