ABSTRACT

In this article, we consider a special class of generalized Nash equilibrium problems that cannot be reduced to a single player control problem. We find a sufficient condition, that proves the existence and uniqueness of solutions. Problems of this type can be solved by a semi-smooth Newton method. Applying the same condition as needed for the uniqueness of solutions, we derive superlinear convergence for the associated Newton method and the equivalent active-set method. We also provide detailed finite element discretizations for both methods. Numerical examples are presented to support the theoretical findings.

中文翻译：

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论不可约多人控制问题的唯一性

摘要

在本文中，我们考虑了一类特殊的广义纳什均衡问题，它们不能简化为单人控制问题。我们找到一个充分条件，证明解的存在性和唯一性。这种类型的问题可以通过半光滑牛顿法来解决。应用解唯一性所需的相同条件，我们推导出关联牛顿法和等效活动集法的超线性收敛。我们还为这两种方法提供了详细的有限元离散化。给出了数值例子来支持理论发现。