【作者】 李靖；

【导师】 屈彪；

【作者基本信息】 曲阜师范大学 ， 运筹学与控制论， 2008， 硕士

【摘要】 本文主要研究广义Nash均衡问题的算法及应用.文中,我们给出了求解该问题的两种算法并对其应用进行了研究.全文共分为四章.第一章是序言,主要介绍了广义Nash均衡问题的研究现状以及本文的主要研究工作.第二章我们给出了求解广义Nash均衡问题的一种混合算法.首先,我们将广义Nash均衡问题转化为一个无约束最优化问题,然后给出一种混合算法来求解这个无约束优化问题,并证明了该算法的全局收敛性.第三章研究了拟变分不等式问题的一种投影算法及其收敛性.由于广义Nash均衡问题可等价转化为一个拟变分不等式问题,因此,该算法也可用于求解广义Nash均衡问题.与文献[18]Noor的算法相比,该算法的优点在于:修正了Noor的算法用于解决一般的拟变分不等式问题,适用范围更广,在更弱的条件下保证了算法的收敛性,而且迭代公式的结构也更为简易.第四章主要对广义Nash均衡问题的应用进行研究.介绍了广义Nash均衡问题在经济、网络切换、环境污染治理、以及交通网络等模型中的应用.更多还原

【Abstract】 In this diss(?)rtation, wo mainly investigate the algorithms and applications of the generalized Nash equilibrium problem. We design two methods for solving the generalized Nash equilibrium problem(GNEP). Also the applications of it are listed in this paper. Four main chapters are included as follows:Chapter 1 is the introduction. We describe the research situations of the generalized Nash equilibrium problem. The main contributions of this paper are also stated briefly.In Chapter 2,we present a new hybrid method for GNEP . At first, we reformulate generalized Nash equilibrium problem into an unconstrained optimization problem ,and then propose a new method for the unconstrained optimization problems and prove the global convergence.In Chapter 3, we design a projection algorithm for quasi-variational Inequalities and prove the global convergence of the algorithms.Due to generalized Nash equilibrium problem can be reformulated into a quasi-variational Inequality,so the method also can be applied to solve the generalized Nash equilibrium. Comparing with Noor’s methods, the superiority of this method is that the application scope of it is more broader.Under a weaker condition the global convergence is guaranteed.And the iterative form is relatively simple.In Chapter 4,we mainly investigate the applications of the generalized Nash equilibrium problem. We introduce the specific applications of the generalized Nash equilibrium problem in abstract economy by Arrow and Dcbrcu,intcrnctswitching,environmental pollution control , the traffic internet switching and so on.更多还原