中文摘要：

通过对函数的泰勒展开式进行误差分析, 提出了对二次模型进行改进的新模型, 在此基础上得到了改进的拟牛顿条件, 并得到了与其相应的Broyden-Fletcher-Goldfarb-Shanno （BFGS）算法. 证明了在适当条件下该算法全局收敛. 从试验函数库中选择标准测试函数, 对经典的BFGS算法与改进的BFGS算法进行数值试验, 试验结果表明改进的算法优于经典的BFGS算法.

英文摘要：

Based on the error analysis of the Taylor expansion, a new model for improving the quadratic model is put forward, and the new secant equation and the corresponding Broyden-Fletcher-Goldfarb-Shanno （BFGS） algorithm are obtained. It is shown that under appropriate conditions, the algorithm is globally convergent. Using the standard test function, the classic BFGS algorithm is compared to the modified BFGS algorithm in the numerical test. The experimental results show that the modified algorithm is better than the classic BFGS algorithm.