Publication
Fractional gradient methods via ψ-Hilfer derivative
dc.contributor.author | Vieira, N. | |
dc.contributor.author | Rodrigues, M. M. | |
dc.contributor.author | Ferreira, M. | |
dc.date.accessioned | 2023-04-11T09:00:03Z | |
dc.date.available | 2023-04-11T09:00:03Z | |
dc.date.issued | 2023-03 | |
dc.description | The 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/2504-3110/7/3/275 | pt_PT |
dc.description | Acknowledgements: 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.abstract | Motivated 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.version | info:eu-repo/semantics/publishedVersion | pt_PT |
dc.identifier.citation | Vieira, 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/fractalfract7030275 | pt_PT |
dc.identifier.doi | https://doi.org/10.3390/fractalfract7030275 | pt_PT |
dc.identifier.eissn | 2504-3110 | |
dc.identifier.other | 275 | |
dc.identifier.uri | http://hdl.handle.net/10400.8/8358 | |
dc.language.iso | eng | pt_PT |
dc.peerreviewed | yes | pt_PT |
dc.publisher | MDPI | pt_PT |
dc.relation | Center for Research and Development in Mathematics and Applications | |
dc.relation | Center for Research and Development in Mathematics and Applications | |
dc.relation | Not Available | |
dc.relation.publisherversion | https://www.mdpi.com/2504-3110/7/3/275 | pt_PT |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | pt_PT |
dc.subject | Fractional calculus | pt_PT |
dc.subject | ψ-Hilfer fractional derivative | pt_PT |
dc.subject | Fractional Gradient method | pt_PT |
dc.subject | Optimization | pt_PT |
dc.title | Fractional gradient methods via ψ-Hilfer derivative | pt_PT |
dc.type | journal article | |
dspace.entity.type | Publication | |
oaire.awardTitle | Center for Research and Development in Mathematics and Applications | |
oaire.awardTitle | Center for Research and Development in Mathematics and Applications | |
oaire.awardTitle | Not Available | |
oaire.awardURI | info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F04106%2F2020/PT | |
oaire.awardURI | info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F04106%2F2020/PT | |
oaire.awardURI | info:eu-repo/grantAgreement/FCT/CEEC IND 2018/CEECIND%2F01131%2F2018%2FCP1559%2FCT0014/PT | |
oaire.citation.issue | 3 | pt_PT |
oaire.citation.title | Fractal and Fractional | pt_PT |
oaire.citation.volume | 7 | pt_PT |
oaire.fundingStream | 6817 - DCRRNI ID | |
oaire.fundingStream | 6817 - DCRRNI ID | |
oaire.fundingStream | CEEC IND 2018 | |
person.familyName | Vieira | |
person.familyName | Rodrigues | |
person.familyName | Ferreira | |
person.givenName | Nelson | |
person.givenName | M. Manuela | |
person.givenName | Milton | |
person.identifier.ciencia-id | 9418-DDFB-DE9D | |
person.identifier.ciencia-id | 461D-A5E2-23BE | |
person.identifier.ciencia-id | CA19-2009-F26D | |
person.identifier.orcid | 0000-0001-8756-4893 | |
person.identifier.orcid | 0000-0002-8834-5841 | |
person.identifier.orcid | 0000-0003-1816-8293 | |
person.identifier.rid | H-9130-2013 | |
person.identifier.rid | A-2004-2015 | |
person.identifier.scopus-author-id | 55576073000 | |
person.identifier.scopus-author-id | 22835991500 | |
person.identifier.scopus-author-id | 12144179800 | |
project.funder.identifier | http://doi.org/10.13039/501100001871 | |
project.funder.identifier | http://doi.org/10.13039/501100001871 | |
project.funder.identifier | http://doi.org/10.13039/501100001871 | |
project.funder.name | Fundação para a Ciência e a Tecnologia | |
project.funder.name | Fundação para a Ciência e a Tecnologia | |
project.funder.name | Fundação para a Ciência e a Tecnologia | |
rcaap.rights | openAccess | pt_PT |
rcaap.type | article | pt_PT |
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