The gradient descent method from the perspective of fractional calculus
Abstract
Motivated by gradient methods in optimization theory, we give methods based on ψ‐fractional derivatives of order α 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 ψ‐fractional derivatives. Numerical examples using the ABM method show that the fractional order α and weight ψ are tunable parameters, which can be helpful for improving the performance of gradient descent methods.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Dec 21, 2020
- Source ID
- 10.1002/mma.7127
Entities
People
- Joel A. Rosenfeld
- Pham Viet Hai
Organizations
- Air Force Office of Scientific Research
- National Science Foundation
- University of South Florida