中文摘要：

本文应用最优化方法求解经济学中的经典问题-竞争市场均衡问题.本文对Ye的算法（Ye首先提出了解Fisher问题的原始-对偶路径跟踪算法）做了改进,分别给出了步长调整和迭代方向分解后的原始-对偶路径跟踪算法,并对算法做了理论证明和复杂性分析.最后分析了初始点的求法,做了初步的数值计算.计算结果表明算法能在有效时间内求得问题的解.

英文摘要：

In this paper we solve the classic competitive market equilibrium problems of the economics by using optimization method. This paper modifies Ye＇s Algorithm （Ye firstly used primal-dual path-following interior point algorithm to study competitive market equilibrium problems ）, we design new primal-dual path-following interior point algorithm by adjusting the step size and decomposing iterative direction, then analyze complexity of our algorithm and give theoretical proof. At last we analyze how to find the start point, and do some elementary computational exercises. The results suggest that our algorithms can get the solution of the problem in valid time.