Please use this identifier to cite or link to this item:
http://hdl.handle.net/10773/36752
Title: | Fractional gradient methods via ψ-Hilfer derivative |
Author: | Vieira, N. Rodrigues, M. M. Ferreira, M. |
Keywords: | Fractional calculus $\psi$-Hilfer fractional derivative Fractional gradient method Optimization |
Issue Date: | Mar-2023 |
Publisher: | MDPI |
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. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/36752 |
DOI: | 10.3390/fractalfract7030275 |
Publisher Version: | https://www.mdpi.com/2504-3110/7/3/275 |
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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