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Fractional gradient methods via ψ-Hilfer derivative

dc.contributor.authorVieira, N.
dc.contributor.authorRodrigues, M. M.
dc.contributor.authorFerreira, M.
dc.date.accessioned2023-04-11T09:00:03Z
dc.date.available2023-04-11T09:00:03Z
dc.date.issued2023-03
dc.descriptionThe final version is published in Fractal and Fractional, 7-No.3, (2023), Article No.275 (30pp.). It as available via the website https://www.mdpi.com/2504-3110/7/3/275pt_PT
dc.descriptionAcknowledgements: The work of the authors was supported by Portuguese funds through CIDMA–Center for Research and Development in Mathematics and Applications, and FCT–Fundação para a Ciência e a Tecnologia, within projects UIDB/04106/2020 and UIDP/04106/2020. N. Vieira was also supported by FCT via the 2018 FCT program of Stimulus of Scientific Employment - Individual Support (Ref: CEECIND/01131/2018).pt_PT
dc.description.abstractMotivated by the increasing of practical applications in fractional calculus, we study the classical gradient method under the perspective of the ψ-Hilfer derivative. This allows us to cover in our study several definitions of fractional derivatives that are found in the literature. The convergence of the ψ-Hilfer continuous fractional gradient method is studied both for strongly and non-strongly convex cases. Using a series representation of the target function, we develop an algorithm for the ψ-Hilfer fractional order gradient method. The numerical method obtained by truncating higher-order terms was tested and analyzed using benchmark functions. Considering variable order differentiation and optimizing the step size, the ψ-Hilfer fractional gradient method shows better results in terms of speed and accuracy. Our results generalize previous works in the literature.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationVieira, N., Rodrigues, M. M., & Ferreira, M. (2023). Fractional Gradient Methods via ψ-Hilfer Derivative. Fractal and Fractional, 7(3), 275. https://doi.org/10.3390/fractalfract7030275pt_PT
dc.identifier.doihttps://doi.org/10.3390/fractalfract7030275pt_PT
dc.identifier.eissn2504-3110
dc.identifier.other275
dc.identifier.urihttp://hdl.handle.net/10400.8/8358
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherMDPIpt_PT
dc.relationCenter for Research and Development in Mathematics and Applications
dc.relationCenter for Research and Development in Mathematics and Applications
dc.relationNot Available
dc.relation.publisherversionhttps://www.mdpi.com/2504-3110/7/3/275pt_PT
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/pt_PT
dc.subjectFractional calculuspt_PT
dc.subjectψ-Hilfer fractional derivativept_PT
dc.subjectFractional Gradient methodpt_PT
dc.subjectOptimizationpt_PT
dc.titleFractional gradient methods via ψ-Hilfer derivativept_PT
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleCenter for Research and Development in Mathematics and Applications
oaire.awardTitleCenter for Research and Development in Mathematics and Applications
oaire.awardTitleNot Available
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F04106%2F2020/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F04106%2F2020/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/CEEC IND 2018/CEECIND%2F01131%2F2018%2FCP1559%2FCT0014/PT
oaire.citation.issue3pt_PT
oaire.citation.titleFractal and Fractionalpt_PT
oaire.citation.volume7pt_PT
oaire.fundingStream6817 - DCRRNI ID
oaire.fundingStream6817 - DCRRNI ID
oaire.fundingStreamCEEC IND 2018
person.familyNameVieira
person.familyNameRodrigues
person.familyNameFerreira
person.givenNameNelson
person.givenNameM. Manuela
person.givenNameMilton
person.identifier.ciencia-id9418-DDFB-DE9D
person.identifier.ciencia-id461D-A5E2-23BE
person.identifier.ciencia-idCA19-2009-F26D
person.identifier.orcid0000-0001-8756-4893
person.identifier.orcid0000-0002-8834-5841
person.identifier.orcid0000-0003-1816-8293
person.identifier.ridH-9130-2013
person.identifier.ridA-2004-2015
person.identifier.scopus-author-id55576073000
person.identifier.scopus-author-id22835991500
person.identifier.scopus-author-id12144179800
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsopenAccesspt_PT
rcaap.typearticlept_PT
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