基于递归型神经网络动力学求解时变凸二次规划

doi:10.15960/j.cnki.issn.1007-6093.2023.01.007

摘要/Abstract

摘要：

为了在线求解时变凸二次规划问题，实现误差精度更高、求解时间更短和收敛速度更快的目标。本文采用了求解问题更快的时变网络设计参数，选择了有限时间可以收敛的Sign-bi-power激活函数，构造了一种改进的归零神经网络动力学模型。其后，分析了模型的稳定性和收敛性，得到其解能够在有限时间内收敛。最后，在仿真算例中，与传统的梯度神经网络和归零神经网络模型相比，所提模型具有更高的误差精度、更短的求解时间和更快的收敛速度，优于前两种网络模型。

关键词: 时变凸二次规划, 改进的归零动力学模型, Sign-bi-power

Abstract:

When solving a time-varying convex quadratic programming problem online, in order to achieve the requirements of higher error accuracy, shorter solution time and faster convergence speed, this paper designs and constructs an improved zeroing neurodynamic model of the design parameters of the time-varying network. Firstly, the Lyapunov stability theory proves that the network model is globally progressively stable. Subsequently, it is proved that when it uses the Sign-bi-power activation function, it is guaranteed that its solution can converge for a finite time. Finally, in the simulation example, compared with the gradient neural network model and the zeroing neural network model, the zeroing neurodynamics of the time-varying network design parameters is better than the two network models in solving the time-convex quadratic programming problem, with higher error accuracy, shorter solution time and faster convergence speed.

Key words: time-varying convex quadratic programming, improved zeroing dynamic model, Sign-bi-power

中图分类号:

TP183
O221

廖伍代, 周军. 基于递归型神经网络动力学求解时变凸二次规划[J]. 运筹学学报, 2023, 27(1): 103-114.

Wudai LIAO, Jun ZHOU. Recurrent neural network dynamic for time-varying convex quadratic programming[J]. Operations Research Transactions, 2023, 27(1): 103-114.

图/表 3

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