In this Letter, by following Zhang et al. is method, a recurrent neural network (termed as Zhang neural network, ZNN) is developed and analyzed for solving online the time-varying convex quadraticprogramming problem subject to time-varying linear-equality constraints. Different from conventional gradient-based neural networks (GNN), such a ZNN model makes full use of the time-derivative information of time-varying coefficient. The resultant ZNN model is theoretically proved to have global exponential convergence to the time-varying theoretical optimal solution of the investigated time-varying convex quadratic program. Computer-simulation results further substantiate the effectiveness, efficiency and novelty of such ZNN model and method.

本论文揭示，作为两种并行的神经计算模型，BP和Hopfield类型神经网络都可以有效地对二次型V（x）=T/2+TVxxPxqx实现最小化求解。而且，尽管BP和Hopfield类型神经网络在网络设计思想和网络结构上呈现出很大的差异，但是它们在二次型函数最小化问题上都表现出了相同的学习能力，这说明两者具有本质的联系。

为避免权值反复迭代修正的冗长BP训练过程，避免传统方法陷入局部极小点，根据多项式理论，构造了一种新型前向神经网络模型，推导了基于最速下降法的误差反传算法和基于伪逆的直接确定法。仿真结果显示，迭代方法和伪逆直接确定法都能达到比较高的工作精度（10-6）。

基于函数逼近理论，构造一种Chebyshev基函数神经网络模型。推导出该网络模型的权值直接确定方法，可一步计算出权值，克服了传统BP神经网络学习率选取困难、学习过程冗长和易陷入局部极小等缺点。在此基础上，设计了基于二分搜索的结构自适应算法，根据精度要求自动确定网络最优结构。理论分析及仿真验证均表明，该网络不仅能够快速地完成网络权值确定和结构自适应，且具有优异的学习与逼近能力，而且对随机加性噪声也具有较好的抑制作用。

In view of parallel-processing nature and circuit-implementation convenience, recurrent neural networks are often employed to solve optimization problems. Recently, a primal-dual neural network based on linear variational inequalities (LVI) was developed by Zhang et al. for the online solution of linear-programming (LP) and quadratic-programming (QP) problems simultaneously subject to equality, inequality and bound constraints. For the final purpose of field programmable gate array (FPGA) and application-specific integrated circuit (ASIC) realization, we investigate in this paper the MATLAB Simulink modeling and simulative verification of such an LVI-based primal-dual neural network (LVI-PDNN). By using click-and-drag mouse operations in MATLAB Simulink environment, we could quickly model and simulate complicated dynamic systems. Modeling and simulative results substantiate the theoretical analysis and efficacy of the LVI-PDNN for solving online the linear and quadratic programs.