A nonlinear preconditioner for optimum experimental design problems

We show how to efficiently compute A-optimal experimental designs, which are formulated in terms of the minimization of the trace of the covariance matrix of the underlying regression process, using quasi-Newton sequential quadratic programming methods. In particular, we introduce a modification of...

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Autores principales:	Mario S. Mommer, Andreas Sommer, Johannes P. Schlöder, H. Georg Bock
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2015
Materias:	90C30 90C55 62K99 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/5227be4f681c41179ccb2281a60abe78
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spelling	oai:doaj.org-article:5227be4f681c41179ccb2281a60abe782021-12-02T05:00:43ZA nonlinear preconditioner for optimum experimental design problems2192-440610.1007/s13675-015-0036-9https://doaj.org/article/5227be4f681c41179ccb2281a60abe782015-05-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2192440621000423https://doaj.org/toc/2192-4406We show how to efficiently compute A-optimal experimental designs, which are formulated in terms of the minimization of the trace of the covariance matrix of the underlying regression process, using quasi-Newton sequential quadratic programming methods. In particular, we introduce a modification of the problem that leads to significantly faster convergence. To derive this modification, we model each iteration in terms of an initial experimental design that is to be improved, and show that the absolute condition number of the model problem grows without bounds as the quality of the initial design improves. As a remedy, we devise a preconditioner that ensures that the absolute condition number will instead stay uniformly bounded. Using numerical experiments, we study the effect of this reformulation on relevant cases of the general problem class, and find that it leads to significant improvements in both stability and convergence behavior.Mario S. MommerAndreas SommerJohannes P. SchlöderH. Georg BockElsevierarticle90C3090C5562K99Applied mathematics. Quantitative methodsT57-57.97Electronic computers. Computer scienceQA75.5-76.95ENEURO Journal on Computational Optimization, Vol 3, Iss 2, Pp 131-146 (2015)
institution	DOAJ
collection	DOAJ
language	EN
topic	90C30 90C55 62K99 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
spellingShingle	90C30 90C55 62K99 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95 Mario S. Mommer Andreas Sommer Johannes P. Schlöder H. Georg Bock A nonlinear preconditioner for optimum experimental design problems
description	We show how to efficiently compute A-optimal experimental designs, which are formulated in terms of the minimization of the trace of the covariance matrix of the underlying regression process, using quasi-Newton sequential quadratic programming methods. In particular, we introduce a modification of the problem that leads to significantly faster convergence. To derive this modification, we model each iteration in terms of an initial experimental design that is to be improved, and show that the absolute condition number of the model problem grows without bounds as the quality of the initial design improves. As a remedy, we devise a preconditioner that ensures that the absolute condition number will instead stay uniformly bounded. Using numerical experiments, we study the effect of this reformulation on relevant cases of the general problem class, and find that it leads to significant improvements in both stability and convergence behavior.
format	article
author	Mario S. Mommer Andreas Sommer Johannes P. Schlöder H. Georg Bock
author_facet	Mario S. Mommer Andreas Sommer Johannes P. Schlöder H. Georg Bock
author_sort	Mario S. Mommer
title	A nonlinear preconditioner for optimum experimental design problems
title_short	A nonlinear preconditioner for optimum experimental design problems
title_full	A nonlinear preconditioner for optimum experimental design problems
title_fullStr	A nonlinear preconditioner for optimum experimental design problems
title_full_unstemmed	A nonlinear preconditioner for optimum experimental design problems
title_sort	nonlinear preconditioner for optimum experimental design problems
publisher	Elsevier
publishDate	2015
url	https://doaj.org/article/5227be4f681c41179ccb2281a60abe78
work_keys_str_mv	AT mariosmommer anonlinearpreconditionerforoptimumexperimentaldesignproblems AT andreassommer anonlinearpreconditionerforoptimumexperimentaldesignproblems AT johannespschloder anonlinearpreconditionerforoptimumexperimentaldesignproblems AT hgeorgbock anonlinearpreconditionerforoptimumexperimentaldesignproblems AT mariosmommer nonlinearpreconditionerforoptimumexperimentaldesignproblems AT andreassommer nonlinearpreconditionerforoptimumexperimentaldesignproblems AT johannespschloder nonlinearpreconditionerforoptimumexperimentaldesignproblems AT hgeorgbock nonlinearpreconditionerforoptimumexperimentaldesignproblems
_version_	1718400827785216000

A nonlinear preconditioner for optimum experimental design problems

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