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The gradient descent method from the perspective of fractional calculus
- Source :
- Mathematical Methods in the Applied Sciences. 44:5520-5547
- Publication Year :
- 2020
- Publisher :
- Wiley, 2020.
-
Abstract
- Motivated by gradient methods in optimization theory, we give methods based on $\psi$-fractional derivatives of order $\alpha$ in order to solve unconstrained optimization problems. The convergence of these methods is analyzed in detail. This paper also presents an Adams-Bashforth-Moulton (ABM) method for the estimation of solutions to equations involving $\psi$-fractional derivatives. Numerical examples using the ABM method show that the fractional order $\alpha$ and weight $\psi$ are tunable parameters, which can be helpful for improving the performance of gradient descent methods.<br />Comment: 27 pages
- Subjects :
- General Mathematics
010102 general mathematics
General Engineering
Order (ring theory)
Unconstrained optimization
01 natural sciences
Fractional calculus
010101 applied mathematics
Perspective (geometry)
Optimization and Control (math.OC)
Convergence (routing)
FOS: Mathematics
Applied mathematics
0101 mathematics
Gradient descent
Mathematics - Optimization and Control
Gradient method
Mathematics
Subjects
Details
- ISSN :
- 10991476 and 01704214
- Volume :
- 44
- Database :
- OpenAIRE
- Journal :
- Mathematical Methods in the Applied Sciences
- Accession number :
- edsair.doi.dedup.....0b729242d361fed965b40913847cb4a6