A curvilinear search using tridiagonal secant updates for unconstrained optimization

The idea of doing a curvilinear search along the Levenberg- Marquardt path s(μ) = - (H + μI)⁻¹g always has been appealing, but the cost of solving a linear system for each trial value of the parameter y has discouraged its implementation. In this paper, an algorithm for searching along a path which...

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Autores principales: Dennis Jr., J.E., Echebest, Nélida Ester, Guardarucci, María Teresa, Martínez, J. M., Scolnik, Hugo Daniel, Vacchino, María Cristina
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 1991
Materias:
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/149690
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id I19-R120-10915-149690
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Unconstrained optimization
Trust regions
Curvilinear search
Levenberg-Marquardt
Factor updating
Least change secant methods
spellingShingle Matemática
Unconstrained optimization
Trust regions
Curvilinear search
Levenberg-Marquardt
Factor updating
Least change secant methods
Dennis Jr., J.E.
Echebest, Nélida Ester
Guardarucci, María Teresa
Martínez, J. M.
Scolnik, Hugo Daniel
Vacchino, María Cristina
A curvilinear search using tridiagonal secant updates for unconstrained optimization
topic_facet Matemática
Unconstrained optimization
Trust regions
Curvilinear search
Levenberg-Marquardt
Factor updating
Least change secant methods
description The idea of doing a curvilinear search along the Levenberg- Marquardt path s(μ) = - (H + μI)⁻¹g always has been appealing, but the cost of solving a linear system for each trial value of the parameter y has discouraged its implementation. In this paper, an algorithm for searching along a path which includes s(μ) is studied. The algorithm uses a special inexpensive QTcQT to QT₊QT Hessian update which trivializes the linear algebra required to compute s(μ). This update is based on earlier work of Dennis-Marwil and Martinez on least-change secant updates of matrix factors. The new algorithm is shown to be local and q-superlinearily convergent to stationary points, and to be globally q-superlinearily convergent for quasi-convex functions. Computational tests are given that show the new algorithm to be robust and efficient.
format Articulo
Preprint
author Dennis Jr., J.E.
Echebest, Nélida Ester
Guardarucci, María Teresa
Martínez, J. M.
Scolnik, Hugo Daniel
Vacchino, María Cristina
author_facet Dennis Jr., J.E.
Echebest, Nélida Ester
Guardarucci, María Teresa
Martínez, J. M.
Scolnik, Hugo Daniel
Vacchino, María Cristina
author_sort Dennis Jr., J.E.
title A curvilinear search using tridiagonal secant updates for unconstrained optimization
title_short A curvilinear search using tridiagonal secant updates for unconstrained optimization
title_full A curvilinear search using tridiagonal secant updates for unconstrained optimization
title_fullStr A curvilinear search using tridiagonal secant updates for unconstrained optimization
title_full_unstemmed A curvilinear search using tridiagonal secant updates for unconstrained optimization
title_sort curvilinear search using tridiagonal secant updates for unconstrained optimization
publishDate 1991
url http://sedici.unlp.edu.ar/handle/10915/149690
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