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http://hdl.handle.net/10773/36752
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DC Field | Value | Language |
---|---|---|
dc.contributor.author | Vieira, N. | pt_PT |
dc.contributor.author | Rodrigues, M. M. | pt_PT |
dc.contributor.author | Ferreira, M. | pt_PT |
dc.date.accessioned | 2023-03-30T15:09:33Z | - |
dc.date.available | 2023-03-30T15:09:33Z | - |
dc.date.issued | 2023-03 | - |
dc.identifier.uri | http://hdl.handle.net/10773/36752 | - |
dc.description.abstract | Motivated by the increasing of practical applications in fractional calculus, we study the classical gradient method under the perspective of the $\psi$-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 $\psi$-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 $\psi$-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 $\psi$-Hilfer fractional gradient method shows better results in terms of speed and accuracy. Our results generalize previous works in the literature. | pt_PT |
dc.language.iso | eng | pt_PT |
dc.publisher | MDPI | pt_PT |
dc.relation | info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F04106%2F2020/PT | pt_PT |
dc.relation | info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F04106%2F2020/PT | pt_PT |
dc.relation | info:eu-repo/grantAgreement/FCT/CEEC IND 2018/CEECIND%2F01131%2F2018%2FCP1559%2FCT0014/PT | pt_PT |
dc.rights | openAccess | pt_PT |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | pt_PT |
dc.subject | Fractional calculus | pt_PT |
dc.subject | $\psi$-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 | article | pt_PT |
dc.description.version | published | pt_PT |
dc.peerreviewed | yes | pt_PT |
degois.publication.firstPage | 1 | pt_PT |
degois.publication.issue | 3 | pt_PT |
degois.publication.lastPage | 30 | pt_PT |
degois.publication.title | Fractal and Fractional | pt_PT |
degois.publication.volume | 7 | pt_PT |
dc.relation.publisherversion | https://www.mdpi.com/2504-3110/7/3/275 | pt_PT |
dc.identifier.doi | 10.3390/fractalfract7030275 | pt_PT |
dc.identifier.essn | 2504-3110 | pt_PT |
dc.identifier.articlenumber | 275 | pt_PT |
Appears in Collections: | CIDMA - Artigos CHAG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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artigo76.pdf | NVMRMF_FF_2023 | 2.01 MB | Adobe PDF | View/Open |
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