Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization |
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Authors: | E. G. Birgin J. M. Martínez |
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Affiliation: | 1.Department of Computer Science IME-USP,University of S?o Paulo,S?o Paulo,Brazil;2.Department of Applied Mathematics, IMECC-UNICAMP,University of Campinas,Campinas,Brazil |
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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. |
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Keywords: | Nonlinear programming Augmented Lagrangian methods Box constraints Quasi-Newton Truncated-Newton |
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