网络均衡问题均衡流的适定性分析

There are a lot of network equilibrium problems in economics, finance, management and engineering systems. The theoretical research and analysis on the equilibrium flow of network equilibrium problems are urgently needed to be in accordance with actual application. Due to the little value of unstable equilibrium flow in the practical application, we propose the research based on the well-posed condition of network equilibrium problems'' equilibrium flow. This project will establish well-posed concepts of network equilibrium problems'' equilibrium flow based on the definition of the approximate equilibrium flow, study well-posed sufficient conditions and equivalent propositions of network equilibrium problems'' equilibrium flow, explore equivalent relations between the well-posedness of network equilibrium problems'' equilibrium flow and the well-posedness of the solution to variational inequality problems, work over the well-posedness of network equilibrium problems'' equilibrium flow by using plenty of research results in the well-posednesss solution to the variational inequality problems, and provide a specific feasible algorithm to form a system of posedness theory of network equilibrium problems'' equilibrium flow from the extensive practical background. This research not only has theoretical significance, but also provide decision guidance for the network equilibrium problems existed in transportation, finance, management and communication systems etc.

在经济、金融、管理及工程系统中大量存在网络均衡问题。对网络均衡问题均衡流的研究迫切需要更加符合实际应用需求的理论研究和分析，针对一个不稳定的均衡流在实际应用中几乎没有价值这个事实， 提出对网络均衡问题均衡流的适定性条件进行研究。本项目拟从网络均衡问题的广泛实际背景出发，探索新概念，在定义网络均衡问题的近似均衡流的基础上，建立其均衡流适定性的概念，研究网络均衡问题均衡流适定的充分性条件和等价命题，探讨网络均衡问题均衡流的适定性与变分不等式问题解的适定性之间的等价关系，并利用目前取得的变分不等式问题解的适定性的研究成果来研究网络均衡问题均衡流的适定性，同时给出具体可行的算法，形成较为系统的网络均衡问题均衡流的适定性理论。本课题研究具有广泛的实际应用价值，其研究成果能为交通运输、金融管理、通讯系统等领域提供决策指导。

本项目从网络均衡问题的广泛实际背景出发，探索新概念，在定义网络均衡问题的近似均衡流的基础上，建立其均衡流适定性的概念，研究网络均衡问题均衡流适定的充分性条件，探讨网络均衡问题均衡流的适定性与变分不等式问题解的适定性之间的等价关系，并利用目前取得的变分不等式问题解的适定性的研究成果来研究网络均衡问题均衡流的适定性。本项目还研究了与课题紧密相关的稳定性分析方面的内容，比如博弈问题的适定性理论，向量平衡问题解集的下半连续性、尖锐性理论。本课题研究具有广泛的实际应用价值，其研究成果能为交通运输、金融管理、通讯系统等领域提供决策指导。