关于求解随机用户均衡问题的截断拟牛顿型信赖域法研究

Discussion on the Truncated Quasi-Newton Type Trust Region Method in Solving the Stochastic User Equilibrium Problem

信赖域法是一种保证全局收敛性的优化算法,为避免Hessian矩阵的计算,基于拟牛顿校正公式构造了求解带线性等式约束的非线性规划问题的截断拟牛顿型信赖域法.首先给出了截断拟牛顿型信赖域法的构造过程及具体步骤;然后针对随机用户均衡模型中变量和约束的特点对算法进行了修正,并将多种拟牛顿校正公式下所得结果与牛顿型信赖域法的结果进行了比较,结果发现基于对称秩1校正公式的信赖域法更为合适.最后基于数值算例结果得到了一些在算法编程过程中的重要结论,对其它形式信赖域法的编程实现具有一定的参考意义.

Trust region method is a global convergence optimization algorithm. In order to avoid the calculation of Hessian matrix, one truncated quasi-Newton trust region method based on the quasi-Newton formula for nonlinear programming problem with linear equality constraints is constructed. First, it gives the construction process of the truncated quasiNewton trust region method and the concrete steps of algorithm. Then several revisions are given for the variable constraints of the stochastic user equilibrium model, and one numerical example is solved. It concludes that the truncated quasi-Newton trust region method based on the symmetric rank one formula is more suitable for stochastic user equilibrium. Finally, some important conclusions are obtained, which can be useful for implementing other forms of trust region method.