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线性控制系统的无界多面体不变集
  • ISSN号：1000-8152
  • 期刊名称：Kongzhi Lilun Yu Yinyong/Control Theory and Applic
  • 时间：0
  • 页码：874-880
  • 分类：O225[理学—运筹学与控制论;理学—数学]
  • 作者机构：[1]大连理工大学数学科学学院,辽宁大连116024
  • 相关基金：基金项目：国家自然科学基金资助项目（11071029;91130007）.
  • 相关项目：关于点集覆盖问题近似算法及其相关问题的研究
作者： 张霞|高岩|夏尊铨|
关键词： 纳什均衡问题, 广义纳什均衡问题, 变分不等式, 半光滑牛顿法, Nash equilibrium problem, generalized Nash equilibrium problem, variational inequality, semismooth Newton method
中文摘要：

应用正则化Nikaido—Isoda函数，一类广义纳什均衡问题的求解被转化为一个极小极大问题的求解．利用Fischer—Burmeister函数将与极小极大问题的必要性条件等价的变分不等式的Karush—Kuhn-Tucker系统转化为一个半光滑方程组．应用牛顿法求解此方程组，并给出了半光滑牛顿法局部超线性收敛的充分条件．数值结果验证了极小极大方法对解决广义纳什均衡问题的有效性．

英文摘要：

Using the regularized Nikaido-Isoda function, the generalized Nash equilibrium problem is reformulated as a minimax problem. Based on Fischer-Burmeister function, the Karush-Kuhn-Tucker system of the variational inequality problem equivalent to the necessary conditions for this minimax problem, is transformed into a semismooth system of equations. The semismooth Newton method is used to solve the system and sufficient conditions for the local superlinear convergence of the semismooth Newton method are derived. Numerical results show that the minimax approach to solving the generalized Nash equilibrium problem is practical.

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期刊信息
  • 《控制理论与应用》
  • 北大核心期刊（2011版）
  • 主管单位:国家教育部
  • 主办单位:华南理工大学 中国科学院数学与系统科学研究院
  • 主编：胡跃明
  • 地址：广州五山路华南理工大学3号楼516室
  • 邮编：510640
  • 邮箱：aukzllyy@scut.edu.cn
  • 电话：020-87111464
  • 国际标准刊号：ISSN：1000-8152
  • 国内统一刊号：ISSN：44-1240/TP
  • 邮发代号:46-11
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  • 被引量:21084