Relaxation Methods for Generalized Nash Equilibrium Problems with Inexact Line Search
Relaxation Methods for Generalized Nash Equilibrium Problems with Inexact Line Search
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DOI：
10.1007/s10957-009-9553-0
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发表时间：
2009-04
影响因子：
1.9
通讯作者：
A. V. Heusinger;Christian Kanzow
中科院分区：
文献类型：
--
作者：
A. V. Heusinger;Christian Kanzow
广义纳什均衡问题（GNEP）是标准纳什博弈的扩展，其中除了成本函数之外，每个参与者的策略空间也取决于所有其他参与者选择的策略。这个问题解决起来比较困难，文献中可用的方法很少。其中最流行的一种是所谓的松弛法，它在一组假设下是全局收敛的。然而，其中一些假设相当有力或有些难以理解。本文提出了求解一类GNEPs的一种改进的松弛方法。收敛分析采用了基于某种下降性质的完全不同的参数，避免了原松弛法的一些技术条件。此外，数值实验表明，改进的松弛方法对文献中许多不同的例子都有很好的效果。
The generalized Nash equilibrium problem (GNEP) is an extension of the standard Nash game where, in addition to the cost functions, also the strategy spaces of each player depend on the strategies chosen by all other players. This problem is rather difficult to solve and there are only a few methods available in the literature. One of the most popular ones is the so-called relaxation method, which is known to be globally convergent under a set of assumptions. Some of these assumptions, however, are rather strong or somewhat difficult to understand. Here, we present a modified relaxation method for the solution of a certain class of GNEPs. The convergence analysis uses completely different arguments based on a certain descent property and avoids some of the technical conditions for the original relaxation method. Moreover, numerical experiments indicate that the modified relaxation method performs quite well on a number of different examples taken from the literature.