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.

中文翻译：

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一种自适应步长的准分数阶梯度下降法及其在系统辨识中的应用

摘要 本文将分数阶梯度法(FOGM)推广到求解高维函数优化问题。提出了一种准分数阶梯度下降法 (QFOGDM)，然后将自适应步长引入 QFOGDM。QFOGDM收敛的理论分析是由三个定理完成的。对求解 15 个无约束优化基准的数值实验进行了比较，以显示其更好的性能。同时，利用所提出的算法对线性离散确定性系统中的参数进行识别，取得了较好的收敛速度和精度。