Gao Xingbao, Du Lili
School of Mathematics and Statistics, Shaanxi Normal University, Xi'an, Shaanxi, 710119, China.
Neural Netw. 2025 Jul;187:107344. doi: 10.1016/j.neunet.2025.107344. Epub 2025 Mar 12.
This paper proposes a novel one-layer neural network to solve quadratic programming problems in real time by using a control parameter and transforming the optimality conditions into a system of projection equations. The proposed network includes two existing dual networks as its special cases, and an existing model can be derived from it. In particular, another new model for linear and quadratic programming problems can be obtained from the proposed network. Meanwhile, a new Lyapunov function is constructed to ensure that the proposed network is Lyapunov stable and can converge to an optimal solution of the concerned problem under mild conditions. In contrast with the existing models for quadratic programming, the proposed network requires the least neurons while maintaining weaker stability conditions. The effectiveness and characteristics of the proposed model are demonstrated by the limited simulation results.
本文提出了一种新颖的单层神经网络，通过使用控制参数并将最优性条件转化为投影方程组来实时求解二次规划问题。所提出的网络包含两个现有的对偶网络作为其特殊情况，并且可以从中推导出一个现有模型。特别地，从所提出的网络可以得到另一个用于线性和二次规划问题的新模型。同时，构造了一个新的李雅普诺夫函数，以确保所提出的网络是李雅普诺夫稳定的，并且在温和条件下能够收敛到相关问题的最优解。与现有的二次规划模型相比，所提出的网络在保持较弱稳定性条件的同时所需神经元最少。有限的仿真结果证明了所提出模型的有效性和特性。
