向量均衡问题的迭代算法研究

项目名称： 向量均衡问题的迭代算法研究

项目编号： No.11201216

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 王三华

作者单位： 南昌大学

项目金额： 22万元

中文摘要： 均衡问题是运筹学的重要研究方向之一。它与力学、微分方程、控制理论、数学经济、最优化理论、对策理论、非线性规划等理论和应用学科有着广泛的联系并有重要的应用。 如何求解，即算法，是均衡问题的一个重要研究方向。目前，尽管有学者对其进行了研究，获得了一些有效的算法，但绝大多数都限于标量均衡问题，而关于向量均衡问题的算法还比较少见。另一方面，向量均衡问题近来受到越来越多学者的关注，一个很重要的原因是真实世界的复杂性，很多实际问题往往需要用多个标准来描述，从而得到向量形式的数学模型。因此，如何建立向量均衡问题的算法是一个有待人们去探索的重要课题。 本项目将着重研究向量均衡问题的迭代算法及其收敛性。这些问题的研究不仅可以丰富和发展向量均衡自身的理论和算法，为向量均衡在交通运输、资源分配、工程管理等领域的应用提供重要理论依据，而且可以促进相关问题的进一步发展，对学科发展有重要意义。

中文关键词： 向量均衡问题；解；存在性；迭代算法；收敛性

英文摘要： Equilibrium problem is one of the most important research aspects in operation research. It is closely related with diverse theoretical and applied disciplines, such as mechanics, partial differential equations, optimal control, mathematical economics, optimization, game theory, nonlinear mathematical programming, etc. And, it is widely applied in these disciplines. How to find a solution is an important research aspect for equilibrium problem. Up to now, many researchers have studied it and obtained quantity effective algorithms. However, to the best of our knowledge, so far most of the algorithms are for scalar equilibrium problem, but very few is for vector one. On the other hand, vector equilibrium problem attracts more and more researchers' attention. One important reason is the complexity of the real world. Usually, the practical problems should be characterized by multiple criterions, and so the vector types of mathematical models are derived. Thus, how to propose appropriate algorithms for vector equilibrium problem is an important project and needs urgently to be explored for people. The main purpose of this project is to study iterative algorithms and their convergence for vector equilibrium problem. The study of these problems will enrich and develop its own theory and algorithm for vector equilibrium

英文关键词： vector equilibrium problem；solution；existence；iterative algorithm；convergence