Maa C Y, Shanblatt M A
Electron. Data Syst., Auburn Hills, MI.
IEEE Trans Neural Netw. 1992;3(4):580-94. doi: 10.1109/72.143372.
Neural networks for linear and quadratic programming are analyzed. The network proposed by M.P. Kennedy and L.O. Chua (IEEE Trans. Circuits Syst., vol.35, pp.554-562, May 1988) is justified from the viewpoint of optimization theory and the technique is extended to solve optimization problems, such as the least-squares problem. For quadratic programming, the network converges either to an equilibrium or to an exact solution, depending on whether the problem has constraints or not. The results also suggest an analytical approach to solve the linear system Bx =b without calculating the matrix inverse. The results are directly applicable to optimization problems with C(2) convex objective functions and linear constraints. The dynamics and applicability of the networks are demonstrated by simulation. The distance between the equilibria of the networks and the problem solutions can be controlled by the appropriate choice of a network parameter.
对用于线性和二次规划的神经网络进行了分析。从优化理论的角度证明了M.P.肯尼迪和L.O.蔡提出的网络（《IEEE电路与系统汇刊》，第35卷，第554 - 562页，1988年5月）的合理性，并将该技术扩展用于解决诸如最小二乘问题等优化问题。对于二次规划，根据问题是否有约束，网络要么收敛到一个平衡点，要么收敛到一个精确解。这些结果还提出了一种无需计算矩阵逆来求解线性系统Bx = b的解析方法。这些结果可直接应用于具有C(2)凸目标函数和线性约束的优化问题。通过仿真演示了网络的动态特性和适用性。通过适当选择网络参数，可以控制网络平衡点与问题解之间的距离。
