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由于标准BP算法是采用均方误差估计器，因而存在易陷入局部极小、收敛速度慢和对初始权敏感等缺陷．本文我们基于Lagrange乘子法和几种稳健解误差估计器，详细研究了一种新的稳健BP的数学理论，得到了稳健BP算法．实验表明：我们提出的算法不仅收敛速度快、对初始权不敏感，而且能够克服“异常值”的影响，对小的噪声振动及过失误差是稳健的．
Because the standard BP algorithm uses the mean square error estimator, it has the defects of easy to fall into local minima, slow convergence rate and sensitive to initial weight. In this paper, based on Lagrange multiplier method and several robust solution error estimators, we study in detail a new mathematical theory of Robust BP and obtain a robust BP algorithm. Experiments show that the proposed algorithm not only converges quickly but is insensitive to initial weights, but also overcomes the influence of “outliers” and is robust to small noise vibration and errors.