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

发布时间：2018-06-03 02:21

本文选题：截断拟牛顿公式 + 信赖域法　；参考：《数学的实践与认识》2017年10期

【摘要】：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.
[Abstract]:The trust region method is an optimal algorithm to guarantee the global convergence. In order to avoid the calculation of the Hessian matrix, a truncated quasi Newton trust region method is constructed to solve the nonlinear programming problem with linear equality constraints based on the quasi Newtonian correction formula. The algorithm is modified by the characteristics of variables and constraints in the stochastic user equilibrium model. The results are compared with the results of Newton type trust region method. The results show that the trust region method based on the symmetric rank 1 correction formula is more suitable. Finally, some algorithms are compiled in the numerical example. The important conclusions in the process are helpful to the programming of other trust region methods.
【作者单位】：济宁学院数学系;
【基金】：国家自然科学基金(71401061)
【分类号】：O224

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