广义纳什均衡问题类乘子算法研究  

Research on the Multiplier-like Algorithm for the Generalized Nash Equilibrium Problem

作　　者：杨迪 YANG Di(Shiyuan College of Nanning Normal University,Nanning,Guangxi Zhuang Autonomous Region,530000 China)

机构地区：[1]南宁师范大学师园学院,广西南宁530000

出　　处：《科技资讯》2023年第10期233-239,共7页Science & Technology Information

基　　金：广西高校中青年科研基础能力项目基金(项目编号:2021KY1750,2019KY0926)。

摘　　要：近年来,许多学者致力于运用精确罚函数法对广义纳什均衡博弈进行研究。该文针对既有等式约束,也有不等式约束的广义纳什均衡问题,根据拉格朗日乘子法思路,给出相同结构类拉格朗日函数,设计了一个类乘子算法,在较弱的情况下,进行可行性和收敛性的分析证明。在具体的数值实验中,该文给出的算法与经典的PHR算法相比较,在时间和迭代步数上都呈现较好的效果,说明算法的有效性。In recent years,many scholars have been studying the generalized Nash equilibrium game by using the exact penalty function method.Aiming at the generalized Nash equilibrium problem with both equality constraints and inequality constraints,this paper gives a Lagrange-like function of the same structure according to the idea of the Lagrangian multiplier method,and designs a multiplier-like algorithm to analyze and prove the feasibility and convergence under weak conditions.In specific numerical experiments,compared with the classical PHR algorithm,the algorithm presented in this paper presents better results in time and iteration steps,indicating the effectiveness of the algorithm.

关 键 词：广义纳什均衡 类乘子算法 拉格朗日算法 精确罚函数 

分 类 号：O225[理学—运筹学与控制论]