基于BFGS公式的改进截断拟牛顿法在随机用户均衡问题上的应用

A modified truncated quasi-Newton method based on BFGS formula for the stochastic user equilibrium problem

根据随机用户均衡问题的特点构造一种基于BFGS校正公式和Armijo线搜索的截断拟牛顿法。介绍截断拟牛顿方程的构造过程及其算法的具体步骤;针对随机用户均衡模型的特点给出算法的收敛性和两个需注意的问题,并将此算法应用于一个路网。数值算例分析表明:所构造算法在迭代次数和误差方面均优于截断牛顿法,改进截断拟牛顿法可以避免二阶Hessian矩阵的计算,还可以用于某些Hessian矩阵不正定问题的求解。

According to the characteristics of stochastic user equilibrium problems,a modified truncated quasi-Newton（ MTQN）method was constructed based on the BFGS correction formula and Armijo line search. The construction process of truncated quasiNewton equation and the concrete steps of the MTQN algorithm were introduced. The convergence and two issues were presented for the characteristics of stochastic user equilibrium model. One numerical example was solved by the MTQN algorithm,and the results were compared with the modified truncated Newton（ MTN） method,which showed that the MTQN was superior to the MTN in both iteration number and absolute error. The modified truncated quasi-Newton method could avoid the computation of the Hessian matrix and could be also applied to solve some special problems when the Hessian matrix was not positive definite.