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: | , , , , , |
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Formato: | Articulo Preprint |
Lenguaje: | Inglés |
Publicado: |
1991
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Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/149690 |
Aporte de: |
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I19-R120-10915-149690 |
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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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bdutipo_str |
Repositorios |
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