讨论了一类基于梯度的监督训练算法及其用于神经网络的参数优化。文中详细讨论了ＬＭ算法，它是梯度下降法与高斯牛顿法的结合，既有高斯牛顿法的局部收敛性，又有梯度下降法的全局特性。μ很大时，ＬＭ算法近似于梯度下降法；μ为零时，则是高斯牛顿法。由于利用了近似的二阶导数信息，ＬＭ算法比梯度法快得多。就训练次数及准确度而言，ＬＭ算法明显优于共轭梯度法和变学习率的ＢＰ算法。由于主矩阵的正定性，解总是存在的，从这种意义上说，ＬＭ算法优于高斯牛顿法 A class of gradient-based supervised training algorithm and its parameter optimization for neural networks are discussed. In this paper, LM algorithm is discussed in detail. It is a combination of gradient descent method and Gauss Newton method, both the local convergence of Gauss Newton method and the global characteristics of gradient descent method. When μ is large, the LM algorithm approximates the gradient descent method; when μ is zero, it is the Gauss Newton method. The LM algorithm is much faster than the gradient method due to the use of approximate second derivative information. In terms of training times and accuracy, the LM algorithm is obviously superior to the BP algorithm with conjugate gradient method and variable learning rate. Due to the positive definiteness of the main matrix, the solution always exists. In this sense, the LM algorithm outperforms the Gauss Newton method