Inexact Restoration method for nonlinear optimization without derivatives

A derivative-free optimization method is proposed for solving a general nonlinear programming problem. It is assumed that the derivatives of the objective function and the constraints are not available. The new method is based on the Inexact Restoration scheme, where each iteration is decomposed in...

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Detalles Bibliográficos
Autores principales:	Arouxét, María Belén, Echebest, Nélida Ester, Pilotta, Elvio Ángel
Formato:	Articulo
Lenguaje:	Inglés
Publicado:	2015
Materias:	Matemática Inexact Restoration Derivative-free optimization Trust-region methods Polynomial interpolation
Acceso en línea:	http://sedici.unlp.edu.ar/handle/10915/94598
Aporte de:	SEDICI (UNLP) de Universidad Nacional de La Plata

id	I19-R120-10915-94598
record_format	dspace
institution	Universidad Nacional de La Plata
institution_str	I-19
repository_str	R-120
collection	SEDICI (UNLP)
language	Inglés
topic	Matemática Inexact Restoration Derivative-free optimization Trust-region methods Polynomial interpolation
spellingShingle	Matemática Inexact Restoration Derivative-free optimization Trust-region methods Polynomial interpolation Arouxét, María Belén Echebest, Nélida Ester Pilotta, Elvio Ángel Inexact Restoration method for nonlinear optimization without derivatives
topic_facet	Matemática Inexact Restoration Derivative-free optimization Trust-region methods Polynomial interpolation
description	A derivative-free optimization method is proposed for solving a general nonlinear programming problem. It is assumed that the derivatives of the objective function and the constraints are not available. The new method is based on the Inexact Restoration scheme, where each iteration is decomposed in two phases. In the first one, the violation of the feasibility is reduced. In the second one, the objective function is minimized onto a linearization of the nonlinear constraints. At both phases, polynomial interpolation models are used in order to approximate the objective function and the constraints. At the first phase a derivative-free solver for box constrained optimization can be used. For the second phase, we propose a new method ad-hoc based on trust-region strategy that uses the projection of the simplex gradient on the tangent space. Under suitable assumptions, the algorithm is well defined and convergence results are proved. A numerical implementation is described and numerical experiments are presented to validate the theoretical results.
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	Inexact Restoration method for nonlinear optimization without derivatives
title_short	Inexact Restoration method for nonlinear optimization without derivatives
title_full	Inexact Restoration method for nonlinear optimization without derivatives
title_fullStr	Inexact Restoration method for nonlinear optimization without derivatives
title_full_unstemmed	Inexact Restoration method for nonlinear optimization without derivatives
title_sort	inexact restoration method for nonlinear optimization without derivatives
publishDate	2015
url	http://sedici.unlp.edu.ar/handle/10915/94598
work_keys_str_mv	AT arouxetmariabelen inexactrestorationmethodfornonlinearoptimizationwithoutderivatives AT echebestnelidaester inexactrestorationmethodfornonlinearoptimizationwithoutderivatives AT pilottaelvioangel inexactrestorationmethodfornonlinearoptimizationwithoutderivatives
bdutipo_str	Repositorios
_version_	1764820491688738818

Inexact Restoration method for nonlinear optimization without derivatives

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