Nonsmooth optimization reformulations of player convex generalized Nash equilibrium problems
Nonsmooth optimization reformulations of player convex generalized Nash equilibrium problems
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DOI：
10.1007/s10898-011-9727-9
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发表时间：
2012-08
影响因子：
1.8
通讯作者：
Axel Dreves;C. Kanzow;O. Stein
中科院分区：
文献类型：
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作者：
Axel Dreves;C. Kanzow;O. Stein
利用正则化的Nikaido-Isoda函数，给出了玩家凸广义纳什均衡问题（GNEP）的（非光滑）约束优化重新表述。进一步，我们给出了一个玩家凸gnep的大子类的无约束的重新表述，特别是包括联合凸gnep。两种方法都将GNEP的所有解描述为优化问题的最小值。详细讨论了这类优化问题的光滑性，并在温和的假设条件下证明了目标函数是连续的和分段连续可微的。本文还给出了一些基于无约束优化重构的数值结果，并将其应用于参与人凸GNEPs。
Using a regularized Nikaido-Isoda function, we present a (nonsmooth) constrained optimization reformulation of the player convex generalized Nash equilibrium problem (GNEP). Further we give an unconstrained reformulation of a large subclass of player convex GNEPs which, in particular, includes the jointly convex GNEPs. Both approaches characterize all solutions of a GNEP as minima of optimization problems. The smoothness properties of these optimization problems are discussed in detail, and it is shown that the corresponding objective functions are continuous and piecewise continuously differentiable under mild assumptions. Some numerical results based on the unconstrained optimization reformulation being applied to player convex GNEPs are also included.