Variable fractional-order gradient descent method

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Journal of Vibration and Shock ›› 2021, Vol. 40 ›› Issue (9) : 43-47.

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

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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.

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fractional-order gradient descent method / variable order / convergence speed / convergence accuracy

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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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