On a derivative-free optimization approach to some problems of civil engineering

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dc.contributor.authorVala, Jiřícs
dc.contributor.authorJarošová, Petracs
dc.coverage.issue1cs
dc.coverage.volume22cs
dc.date.accessioned2024-02-19T13:46:07Z
dc.date.available2024-02-19T13:46:07Z
dc.date.issued2023-09-26cs
dc.description.abstractDevelopment of advanced materials and structures for civil engineering, due to the requirements of green and sustainable building, including the reduction of energy consumption and the balance between occupant comfort and environmental friendliness, needs proper analysis of related physical, chemical, etc. processes, whose mathematical description leads to direct, sensitivity and inverse initial and boundary value problems for nonlinear partial differential equations, analysed numerically using finite element, difference and similar techniques. Design optimization requires to implement a set of additional variable parameters into all related computations, which is very expensive or quite impossible in most cases. Thus realistic computational strategies work with the minimizations of some cost functions with unknown parameters using certain kind of numerical differentiation, like quasi-Newton, inexact Newton or conjugate gradient methods, some derivative-free approach, or, as a much-favoured alternative, some heuristic soft-computing algorithm. A reasonable compromise seems to be the exploitation of an algorithm coming from the non-gradient Nelder-Mead simplex approach. In this paper, referring to the experience with i) the direct problem of thermal design of a residential building and ii) the inverse problem of identification of material characteristics as thermal conductivity and diffusivity from well-Advised laboratory experiments, after several remarks to the history and progress of the Nelder-Mead method and its improvements, we shall demonstrate some convergence properties of such approach, regardless of the highly cited evaluation of the original Nelder-Mead algorithm: "Mathematicians hate it because you cannot prove convergence; engineers seem to love it because it often works.".en
dc.formattextcs
dc.format.extent641-651cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationWSEAS Transactions on Mathematics. 2023, vol. 22, issue 1, p. 641-651.en
dc.identifier.doi10.37394/23206.2023.22.71cs
dc.identifier.issn1109-2769cs
dc.identifier.orcid0000-0003-4837-9622cs
dc.identifier.other186970cs
dc.identifier.researcheridG-2364-2019cs
dc.identifier.scopus57202622116cs
dc.identifier.urihttps://hdl.handle.net/11012/245049
dc.language.isoencs
dc.publisherWSEAScs
dc.relation.ispartofWSEAS Transactions on Mathematicscs
dc.relation.urihttps://wseas.com/journals/mathematics/2023/b445106-033(2023).pdfcs
dc.rightsCreative Commons Attribution 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/1109-2769/cs
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/cs
dc.subjectderivative-free optimizationen
dc.subjectdesign in civil engineeringen
dc.subjectdirect and inverse problemsen
dc.subjectfinite element and difference techniquesen
dc.titleOn a derivative-free optimization approach to some problems of civil engineeringen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-186970en
sync.item.dbtypeVAVen
sync.item.insts2024.02.19 14:46:07en
sync.item.modts2024.02.19 14:12:44en
thesis.grantorVysoké učení technické v Brně. Fakulta stavební. Ústav matematiky a deskriptivní geometriecs
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