AN ALGORITHM FOR THE SPATIAL PRICE EQUILIBRIUM PROBLEM ON A GENERAL NETWORK IN THE SPACE OF THE PATH FLOWS*
针对一般网络上路径流空间的价格均衡问题，提出一种结合高斯-赛德尔-牛顿投影算法与限制策略的求解方法，无需事先生成所有路径，计算结果表明该算法高效。
ABSTRACT. The spatial price equilibrium on a general network may be formulated as a nonlinear‐cost mathematical programming problem with simple constraints, when the decision variables are the path flows. The solution of this problem is difficult due to the very large number of variables (paths) and the impracticality of generating all the paths from all the origins to all the destinations. In this paper, we develop a Gauss‐Seidel‐Newton Projection algorithm and combine it with a restriction strategy. That makes it unnecessary to generate a priori all the paths. This algorithm may be further improved by exploiting the equivalence between the spatial price equilibrium on a general network and the network equilibrium. Computational results that we present in this paper demonstrate the efficiency of the proposed solution algorithms.