Active-set strategy in Powell's method for optimization without derivatives

In this article we present an algorithm for solving bound constrained optimization problems without derivatives based on Powell's method for derivative-free optimization. First we consider the unconstrained optimization problem. At each iteration a quadratic interpolation model of the objective...

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Detalles Bibliográficos
Autores principales: Arouxét, María Belén, Echebest, Nélida Ester, Pilotta, Elvio Ángel
Formato: Articulo
Lenguaje:Inglés
Publicado: 2011
Materias:
Ciencias Exactas
Matemática
active-set method
derivative-free optimization
spectral gradient method
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/40173
http://www.scielo.br/pdf/cam/v30n1/09.pdf
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-40173
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Ciencias Exactas
Matemática
active-set method
derivative-free optimization
spectral gradient method
spellingShingle Ciencias Exactas
Matemática
active-set method
derivative-free optimization
spectral gradient method
Arouxét, María Belén
Echebest, Nélida Ester
Pilotta, Elvio Ángel
Active-set strategy in Powell's method for optimization without derivatives
topic_facet Ciencias Exactas
Matemática
active-set method
derivative-free optimization
spectral gradient method
description In this article we present an algorithm for solving bound constrained optimization problems without derivatives based on Powell's method for derivative-free optimization. First we consider the unconstrained optimization problem. At each iteration a quadratic interpolation model of the objective function is constructed around the current iterate and this model is minimized to obtain a new trial point. The whole process is embedded within a trust-region framework. Our algorithm uses infinity norm instead of the Euclidean norm and we solve a box constrained quadratic subproblem using an active-set strategy to explore faces of the box. Therefore, a bound constrained optimization algorithm is easily extended. We compare our implementation with NEWUOA and BOBYQA, Powell's algorithms for unconstrained and bound constrained derivative free optimization respectively. Numerical experiments show that, in general, our algorithm require less functional evaluations than Powell's algorithms. Mathematical subject classification: Primary: 06B10; Secondary: 06D05.
format Articulo
Articulo
author Arouxét, María Belén
Echebest, Nélida Ester
Pilotta, Elvio Ángel
author_facet Arouxét, María Belén
Echebest, Nélida Ester
Pilotta, Elvio Ángel
author_sort Arouxét, María Belén
title Active-set strategy in Powell's method for optimization without derivatives
title_short Active-set strategy in Powell's method for optimization without derivatives
title_full Active-set strategy in Powell's method for optimization without derivatives
title_fullStr Active-set strategy in Powell's method for optimization without derivatives
title_full_unstemmed Active-set strategy in Powell's method for optimization without derivatives
title_sort active-set strategy in powell's method for optimization without derivatives
publishDate 2011
url http://sedici.unlp.edu.ar/handle/10915/40173
http://www.scielo.br/pdf/cam/v30n1/09.pdf
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AT echebestnelidaester activesetstrategyinpowellsmethodforoptimizationwithoutderivatives
AT pilottaelvioangel activesetstrategyinpowellsmethodforoptimizationwithoutderivatives
bdutipo_str Repositorios
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