改进的DFP优化方法及其在位移反分析中的应用

在常规的DFP方法中引入改进的牛顿迭代下山法，从而在DFP方法中无需执行一维搜索，也可使得初始点不断地向最优点收敛，进而得出最优值。与此同时，还在此方法中采用了数值精度高的理查得外推法公式求梯度。改进后的DFP方法与常规的DFP方法在数值试验和工程应用中进行比较，其对比结果表明：该方法具有更好的数值稳定性、更快的收敛速度及更高的优化结果可靠度。

Extended Davidon-Fletcher-Powell(DFP) optimization method and its application to displacement back analysis

An extended DFP method, in which the modified Newton decent method is used to obtain good variables and Richard extrapolation is used to compute the gradient in each iteration. The single variable search, which the ordinary DFP arithmetic often has to do, is not required in the extended DFP method; but the optimized results can be reached step by step. Numerical test is carried out by both the extended DFP method and the ordinary DFP method; and comparisons of the results demonstrate that the extended DFP method is better than the ordinary DFP method in numerical stability, convergence and reliability.