Artículos de revistas
Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, v.39, n.1, p.1-16, 2008
BIRGIN, E. G.
MARTINEZ, J. M.
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.