期刊
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
卷 357, 期 4, 页码 2514-2532出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jfranklin.2020.01.008
关键词
-
类别
资金
- National Natural Science Foundation of China [61601431, 61973291]
- China Scholarship Council [201806345002]
Fractional calculus is an efficient tool, which has the potential to improve the performance of gradient methods. However, when the first order gradient direction is generalized by fractional order gradient one, the corresponding algorithm converges to the fractional extreme point of the target function which is not equal to the real extreme point. This drawback critically hampers the application of this method. To solve such a convergence problem, the current paper analyzes the specific reasons and proposes three possible solutions. Considering the long memory characteristics of fractional derivative, short memory principle is a prior choice. Apart from the truncation of memory length, two new methods are developed to reach the convergence. The former is the truncation of the infinite series, and the latter is the modification of the constant fractional order. Finally, six illustrative examples are performed to illustrate the effectiveness and practicability of proposed methods. (C) 2020 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据