带BB步长的自适应投影法解广义纳什均衡问题  

A Self-Adaptive Projection Method with the BB-Step Sizes for Solving Generalized Nash Equilibrium Problems

作　　者：毕培培 徐玲玲[1] 韩德仁[1] 

机构地区：[1]南京师范大学数学科学学院,江苏省大规模复杂系统数值模拟重点实验室,南京210023

出　　处：《南京师大学报（自然科学版）》2014年第4期31-40,共10页Journal of Nanjing Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11071122);江苏省自然科学基金(BK2009397);江苏省高校自然科学研究项目(13KJD110007)

摘　　要：广义纳什均衡问题是一种非合作博弈,其每个竞争者的策略集和目标函数都要依靠其他竞争者的策略.它在经济学、管理科学及交通运输等领域都有广泛的应用,但如何有效地求解广义纳什均衡问题仍然是备受关注的课题.本文提出了带有BB步长的自适应投影法求解广义纳什均衡问题:首先,把广义纳什均衡问题转化成拟变分不等式问题,然后把BB步长推广到求解拟变分不等式问题上,并在函数余强制条件下证明了算法的全局收敛性.数值结果进一步说明该方法的有效性.The generalized Nash equilibrium problem（ GNEP） is a noncooperative game in which the strategy set of each player,as well as his payoff function, depend on the rival players ’ strategies. It can be widely used in economics, management sciences and traffic assignment,but how to effective solve the generalized Nash equilibrium problem is still a subject of concern. In this paper, we present a self-adaptive projection method with the BB-step sizes for solving generalized Nash equilibrium problems：First, we give the reformulation of a generalized Nash equilibrium. Then, we extend the BB-step sizes to the QVI formulation of the GNEP,we adopt them in projection methods,and prove that under the condition that the underlying function is co-coercive,the sequence generated by the method converges to a solution of the quasi-variational inequality problem globally. Some preliminary computational results are reported, which illustrate that the new method is efficient.

关 键 词：广义纳什均衡问题 拟变分不等式 投影法 BB步长 收敛性 

分 类 号：O242[理学—计算数学]