A quasi fractional order gradient descent method with adaptive stepsize and its application in system identification

Abstract In this paper, the fractional order gradient method (FOGM) is extended to the solution of high-dimensional function optimization problems. A quasi fractional order gradient descent method (QFOGDM) is proposed and then introduce an adaptive stepsize into QFOGDM. The theoretic analysis for convergence of QFOGDM is be done by three theorems. The numerical experiments for solving 15 unconstrained optimization benchmarks are compared to show its’ better performance. Meanwhile, the proposed algorithm is utilized to identify the parameters in the linear discrete deterministic systems and achieves a better convergence rate and accuracy.