一种带记忆的阻尼牛顿法
A Damping Newton Method with Memory
DOI: 10.12677/aam.2024.136250, PDF,    科研立项经费支持
作者: 路荟平, 奚 杰, 姜志侠*：长春理工大学数学与统计学院，吉林 长春
关键词: 拟牛顿法；阻尼牛顿法；BFGS算法；LBFGS算法；神经网络；Quasi Newton Method； Damping Newton Method； BFGS Algorithm； LBFGS Algorithm； Neural Network
摘要: 本文在引进阻尼技术的基础上构造了新的拟牛顿方程，该方程通过利用相邻两次迭代点之间的梯度差和变化量的线性组合，实现了曲率对的更新，以此改进校正公式。为求解高维问题，引入有限内存记忆框架，提出了D-LBFGS算法。利用D-LBFGS算法对神经网络中的权值阈值参数进行优化的算法，进一步提出了D-LBFGS—CNN算法，在解决无创光谱血糖浓度的预测问题中迭代351次时精度达到99.999%。所提出的D-LBFGS算法在一定程度上优于标准的LBFGS算法(迭代474次时精度99.999%)、阻尼牛顿法(精度99.359%)及文献中的LBFGS算法(精度99.744%)。
Abstract: This paper constructs a new quasi-Newton equation based on the introduction of damping technology. This equation uses the linear combination of the gradient difference and change between two adjacent iteration points to update the curvature pair, thereby improving the correction formula. In order to solve high-dimensional problems, the limited memoryframe work is introduced and the D-LBFGS algorithm is proposed. The D-LBFGS algorithm is used to optimize the weight threshold parameters in the neural network, and the D-LBFGS—CNN algorithm is further proposed. The accuracy reaches 99.999% when iterating 351 times to solve the prediction problem of non-invasive spectral blood glucose concentration. The proposed D-LBFGS algorithm is superior to the standard LBFGS algorithm (accuracy 99.999% at 474 iterations), the damped Newton method (accuracy 99.359%), and the LBFGS algorithm in the literature (accuracy 99.744%) to a certain extent.
文章引用：路荟平, 奚杰, 姜志侠. 一种带记忆的阻尼牛顿法[J]. 应用数学进展, 2024, 13(6): 2614-2626. https://doi.org/10.12677/aam.2024.136250

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