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...
Guardado en:
| Autores principales: | , , , , , |
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| Formato: | Articulo Preprint |
| Lenguaje: | Inglés |
| Publicado: |
1991
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/149690 |
| Aporte de: |
| 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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