变阶次分数阶梯度下降法的研究

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振动与冲击 ›› 2021, Vol. 40 ›› Issue (9) : 43-47.

论文

变阶次分数阶梯度下降法的研究

李佳维1, 2，申永军1, 2，杨绍普1, 2

作者信息 +

Variable fractional-order gradient descent method

LI Jiawei1, 2, SHEN Yongjun1, 2, YANG Shaopu1, 2

Author information +

文章历史 +

摘要

作为经典的凸优化算法，梯度下降法结合分数阶微积分理论，延伸出分数阶梯度下降法。与常规梯度下降法相比，阶次大于1的分数阶梯度下降法收敛速度快但是收敛精度低；而阶次小于1的分数阶梯度下降法收敛精度高但是收敛速度慢。为结合不同阶次分数阶梯度下降法的优点，解决收敛速度、收敛精度之间不可兼得的矛盾，结合已有的研究，为得到更好的优化算法性能，提出了三种改进的变阶次分数阶梯度下降法，并且通过典型算例验证了相关结论。

Abstract

The gradient descent method is a classical convex optimization algorithm.Here, combined with the theory of fractional-order advanced calculus, the fractional-order gradient descent method was investigated.It was shown that compared with the conventional gradient descent method, the fractional-order gradient descent method with the order larger than 1 has faster convergence speed and lower convergence accuracy, while it with the order less than 1 has higher convergence accuracy and slower convergence speed.In order to combine advantages of different fractional-order gradient descent methods and solve the contradiction between convergence speed and convergence accuracy, 3 improved variable fractional-order gradient descent methods were proposed based on the published study results to obtain better optimization algorithm performances.Typical examples were taken to verify relevant conclusions.

导出引用

李佳维1, 2，申永军1, 2，杨绍普1, 2. 变阶次分数阶梯度下降法的研究[J]. 振动与冲击, 2021, 40(9): 43-47

LI Jiawei1, 2, SHEN Yongjun1, 2, YANG Shaopu1, 2. Variable fractional-order gradient descent method[J]. Journal of Vibration and Shock, 2021, 40(9): 43-47

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