A modification of the αBB method for box-constrained optimization and an application to inverse kinematics

For many practical applications it is important to determine not only a numerical approximation of one but a representation of the whole set of globally optimal solutions of a non-convex optimization problem. Then one element of this representation may be chosen based on additional information which...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Gabriele Eichfelder, Tobias Gerlach, Susanne Sumi
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2016
Materias:	90C26 90C30 90C90 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/dfdc2452d7354f9083c06681c39111ce
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:dfdc2452d7354f9083c06681c39111ce
record_format	dspace
spelling	oai:doaj.org-article:dfdc2452d7354f9083c06681c39111ce2021-12-02T05:00:49ZA modification of the αBB method for box-constrained optimization and an application to inverse kinematics2192-440610.1007/s13675-015-0056-5https://doaj.org/article/dfdc2452d7354f9083c06681c39111ce2016-02-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2192440621000563https://doaj.org/toc/2192-4406For many practical applications it is important to determine not only a numerical approximation of one but a representation of the whole set of globally optimal solutions of a non-convex optimization problem. Then one element of this representation may be chosen based on additional information which cannot be formulated as a mathematical function or within a hierarchical problem formulation. We present such an application in the field of robotic design. This application problem can be modeled as a smooth box-constrained optimization problem. We extend the well-known αBB method such that it can be used to find an approximation of the set of globally optimal solutions with a predefined quality. We illustrate the properties and give a proof for the finiteness and correctness of our modified αBB method.Gabriele EichfelderTobias GerlachSusanne SumiElsevierarticle90C2690C3090C90Applied mathematics. Quantitative methodsT57-57.97Electronic computers. Computer scienceQA75.5-76.95ENEURO Journal on Computational Optimization, Vol 4, Iss 1, Pp 93-121 (2016)
institution	DOAJ
collection	DOAJ
language	EN
topic	90C26 90C30 90C90 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
spellingShingle	90C26 90C30 90C90 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95 Gabriele Eichfelder Tobias Gerlach Susanne Sumi A modification of the αBB method for box-constrained optimization and an application to inverse kinematics
description	For many practical applications it is important to determine not only a numerical approximation of one but a representation of the whole set of globally optimal solutions of a non-convex optimization problem. Then one element of this representation may be chosen based on additional information which cannot be formulated as a mathematical function or within a hierarchical problem formulation. We present such an application in the field of robotic design. This application problem can be modeled as a smooth box-constrained optimization problem. We extend the well-known αBB method such that it can be used to find an approximation of the set of globally optimal solutions with a predefined quality. We illustrate the properties and give a proof for the finiteness and correctness of our modified αBB method.
format	article
author	Gabriele Eichfelder Tobias Gerlach Susanne Sumi
author_facet	Gabriele Eichfelder Tobias Gerlach Susanne Sumi
author_sort	Gabriele Eichfelder
title	A modification of the αBB method for box-constrained optimization and an application to inverse kinematics
title_short	A modification of the αBB method for box-constrained optimization and an application to inverse kinematics
title_full	A modification of the αBB method for box-constrained optimization and an application to inverse kinematics
title_fullStr	A modification of the αBB method for box-constrained optimization and an application to inverse kinematics
title_full_unstemmed	A modification of the αBB method for box-constrained optimization and an application to inverse kinematics
title_sort	modification of the αbb method for box-constrained optimization and an application to inverse kinematics
publisher	Elsevier
publishDate	2016
url	https://doaj.org/article/dfdc2452d7354f9083c06681c39111ce
work_keys_str_mv	AT gabrieleeichfelder amodificationoftheabbmethodforboxconstrainedoptimizationandanapplicationtoinversekinematics AT tobiasgerlach amodificationoftheabbmethodforboxconstrainedoptimizationandanapplicationtoinversekinematics AT susannesumi amodificationoftheabbmethodforboxconstrainedoptimizationandanapplicationtoinversekinematics AT gabrieleeichfelder modificationoftheabbmethodforboxconstrainedoptimizationandanapplicationtoinversekinematics AT tobiasgerlach modificationoftheabbmethodforboxconstrainedoptimizationandanapplicationtoinversekinematics AT susannesumi modificationoftheabbmethodforboxconstrainedoptimizationandanapplicationtoinversekinematics
_version_	1718400860641296384

A modification of the αBB method for box-constrained optimization and an application to inverse kinematics

Ejemplares similares