Fractional gradient methods via ψ-Hilfer derivative
| Autor(a) principal: | |
|---|---|
| Data de Publicação: | 2023 |
| Outros Autores: | , |
| Tipo de documento: | Artigo |
| Idioma: | eng |
| Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
| Texto Completo: | http://hdl.handle.net/10400.8/8358 |
Resumo: | 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 |
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Fractional gradient methods via ψ-Hilfer derivativeFractional calculusψ-Hilfer fractional derivativeFractional Gradient methodOptimizationThe 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/2504-3110/7/3/275Acknowledgements: 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).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.MDPIIC-OnlineVieira, N.Rodrigues, M. M.Ferreira, M.2023-04-11T09:00:03Z2023-032023-03-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.8/8358engVieira, 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/fractalfract7030275275https://doi.org/10.3390/fractalfract70302752504-3110info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-01-17T15:57:09Zoai:iconline.ipleiria.pt:10400.8/8358Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:51:05.802206Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
| dc.title.none.fl_str_mv |
Fractional gradient methods via ψ-Hilfer derivative |
| title |
Fractional gradient methods via ψ-Hilfer derivative |
| spellingShingle |
Fractional gradient methods via ψ-Hilfer derivative Vieira, N. Fractional calculus ψ-Hilfer fractional derivative Fractional Gradient method Optimization |
| title_short |
Fractional gradient methods via ψ-Hilfer derivative |
| title_full |
Fractional gradient methods via ψ-Hilfer derivative |
| title_fullStr |
Fractional gradient methods via ψ-Hilfer derivative |
| title_full_unstemmed |
Fractional gradient methods via ψ-Hilfer derivative |
| title_sort |
Fractional gradient methods via ψ-Hilfer derivative |
| author |
Vieira, N. |
| author_facet |
Vieira, N. Rodrigues, M. M. Ferreira, M. |
| author_role |
author |
| author2 |
Rodrigues, M. M. Ferreira, M. |
| author2_role |
author author |
| dc.contributor.none.fl_str_mv |
IC-Online |
| dc.contributor.author.fl_str_mv |
Vieira, N. Rodrigues, M. M. Ferreira, M. |
| dc.subject.por.fl_str_mv |
Fractional calculus ψ-Hilfer fractional derivative Fractional Gradient method Optimization |
| topic |
Fractional calculus ψ-Hilfer fractional derivative Fractional Gradient method Optimization |
| 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 |
| publishDate |
2023 |
| dc.date.none.fl_str_mv |
2023-04-11T09:00:03Z 2023-03 2023-03-01T00:00:00Z |
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info:eu-repo/semantics/publishedVersion |
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info:eu-repo/semantics/article |
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article |
| status_str |
publishedVersion |
| dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.8/8358 |
| url |
http://hdl.handle.net/10400.8/8358 |
| dc.language.iso.fl_str_mv |
eng |
| language |
eng |
| dc.relation.none.fl_str_mv |
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 275 https://doi.org/10.3390/fractalfract7030275 2504-3110 |
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info:eu-repo/semantics/openAccess |
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openAccess |
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application/pdf |
| dc.publisher.none.fl_str_mv |
MDPI |
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MDPI |
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reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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