Augmented penalty algorithms based on BFGS secant approximations and trust regions

Croceri, Graciela M.; Sottosanto, Graciela N.; Maciel, María Cristina

doi:10.1016/j.apnum.2006.04.001

Cited by 5 publications

(2 citation statements)

References 27 publications

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“…In an independent recent report, Groceri, Sottosanto and Maciel [27] proposed a different structured BFGS method for solving Augmented Lagrangian subproblems for equality constraints. They propose a least-change update method in the sense of Dennis and Schnabel [17] which differs from our approach in the amount of information on previous iterations that is kept in the Hessian approximations.…”

Section: Discussionmentioning

confidence: 99%

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

Birgin

Martínez

2007

Comput Optim Appl

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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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Section: Discussionmentioning

confidence: 99%

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

Birgin

Martínez

2007

Comput Optim Appl

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“…Los dos algoritmos que presentamos para resolver (1) están basados en la minimización secuencial del Lagrangiano Aumentado. El método, desarrollado originalmente para resolver el problema de minimización con restricciones de igualdad [11], fue aplicado después a la resolución de problemas de cuadrados mínimos con restricciones de igualdad [6] donde se incorporó una aproximación secante del tipo BFGS [8], [4].…”

Section: F (X)unclassified

omparación de dos algoritmos de lagrangiano aumentado para el problema de optimización con restricciones de igualdad

Croceri¹,

Sottosanto²

2014

MAT

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En este trabajo se presentan dos algoritmos basados en la minimización secuencial del Lagrangiano Aumentado para resolver el problema de optimización con restricciones de igualdad. Uno de los algoritmos combina una técnica de gradiente conjugado y región de confianza. El segundo utiliza como estrategia de resolución un método de gradiente proyectado, y la convergencia desde cualquier punto inicial, se obtiene mediante un esquema tipo Armijo. Un estimado del multiplicador de Lagrange se actualiza en cada iteración y el parámetro de penalización se modifica para obtener suficiente reducción en la norma de las restricciones. La información de segundo orden, en ambos algoritmos, se actualiza mediante una técnica secante. Los algoritmos fueron implementados en Scilab y se reportan resultados numéricos sobre un conjuntos de problemas test de la colección CUTEr.

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Superlinearly Convergent Exact Penalty Methods with Projected Structured Secant Updates for Constrained Nonlinear Least Squares

Bidabadi

Mahdavi–Amiri

2013

J Optim Theory Appl

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Augmented penalty algorithms based on BFGS secant approximations and trust regions

Cited by 5 publications

References 27 publications

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

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

omparación de dos algoritmos de lagrangiano aumentado para el problema de optimización con restricciones de igualdad

Superlinearly Convergent Exact Penalty Methods with Projected Structured Secant Updates for Constrained Nonlinear Least Squares

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