共查询到19条相似文献,搜索用时 62 毫秒
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研究每个局中人的决策集都有可能与竞争者的决策集有关的广义纳什均衡问题.给出了该广义纳什均衡问题罚函数形式的再定式.通过分析其KKT点的特点,进一步给出了求解广义纳什均衡问题的增量罚算法. 相似文献
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关于一类随机变分不等式和随机拟变分不等式问题 总被引:1,自引:0,他引:1
本文对单值和多值情形的随机变分不等式和随机拟变分不等式得出可测解的存在性条件。另外还利用KKM-技巧及著名的Ky Fan定理对一类确定型的广义拟变分不等式讨论了解的存在性问题。本文的结果改进和发展了[10,11,12]中的重要结果。 相似文献
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本文在非常一般的框架下,建立了极大极小不等式,广义变分不等式和广义拟变分不等式,证明了解的存在定理,且它们是在非紧集上得到的,从而推广和改进了[3~13]中的相应结果. 相似文献
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本文引进了映射Q相对于另一映射 T 是下半连续的概念。在此条件下,讨论了广义拟变分不等式的选择映射的连续性问题。并得到了一个广义拟变分不等式解的存在性定理。 相似文献
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Minglu Ye 《Optimization》2017,66(7):1119-1134
The generalized Nash equilibrium problem (GNEP) is an n-person noncooperative game in which each player’s strategy set depends on the rivals’ strategy set. In this paper, we presented a half-space projection method for solving the quasi-variational inequality problem which is a formulation of the GNEP. The difference from the known projection methods is due to the next iterate point in this method is obtained by directly projecting a point onto a half-space. Thus, our next iterate point can be represented explicitly. The global convergence is proved under the minimal assumptions. Compared with the known methods, this method can reduce one projection of a vector onto the strategy set per iteration. Numerical results show that this method not only outperforms the known method but is also less dependent on the initial value than the known method. 相似文献
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The generalized Nash equilibrium problem (GNEP) is a noncooperative game in which the strategy set of each player, as well as his payoff function, depend on the rival players strategies. As a generalization of the standard Nash equilibrium problem (NEP), the GNEP has recently drawn much attention due to its capability of modeling a number of interesting conflict situations in, for example, an electricity market and an international pollution control. In this paper, we propose an improved two-step (a prediction step and a correction step) method for solving the quasi-variational inequality (QVI) formulation of the GNEP. Per iteration, we first do a projection onto the feasible set defined by the current iterate (prediction) to get a trial point; then, we perform another projection step (correction) to obtain the new iterate. Under certain assumptions, we prove the global convergence of the new algorithm. We also present some numerical results to illustrate the ability of our method, which indicate that our method outperforms the most recent projection-like methods of Zhang et al. (2010). 相似文献
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This paper deals with the generalized Nash equilibrium problem (GNEP), i.e. a noncooperative game in which the strategy set
of each player, as well as his payoff function, depends on the strategies of all players. We consider an equivalent optimization
reformulation of GNEP using a regularized Nikaido–Isoda function so that solutions of GNEP coincide with global minima of
the optimization problem. We then propose a derivative-free descent type method with inexact line search to solve the equivalent
optimization problem and we prove that our algorithm is globally convergent. The convergence analysis is not based on conditions
guaranteeing that every stationary point of the optimization problem is a solution of GNEP. Finally, we present the performance
of our algorithm on some examples. 相似文献
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It is well known that the generalized Nash equilibrium problem, a model for multi-leader–follower games, can be reformulated as a quasivariational inequality. We show that, in fact, a reformulation in terms of a variational inequality can be obtained in the general setting of quasiconvex nondifferentiable decision functions. An existence result is deduced. 相似文献
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《Optimization》2012,61(12):2269-2295
ABSTRACTIn this paper, we propose a best-response approach to select an equilibrium in a two-player generalized Nash equilibrium problem. In our model we solve, at each of a finite number of time steps, two independent optimization problems. We prove that convergence of our Jacobi-type method, for the number of time steps going to infinity, implies the selection of the same equilibrium as in a recently introduced continuous equilibrium selection theory. Thus the presented approach is a different motivation for the existing equilibrium selection theory, and it can also be seen as a numerical method. We show convergence of our numerical scheme for some special cases of generalized Nash equilibrium problems with linear constraints and linear or quadratic cost functions. 相似文献
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The generalized Nash equilibrium problem (GNEP) is a generalization of the standard Nash equilibrium problem (NEP),in which both the utility function and the strategy space of each player depend on the strategies chosen by all other players.This problem has been used to model various problems in applications.However,the convergent solution algorithms are extremely scare in the literature.In this paper,we present an incremental penalty method for the GNEP,and show that a solution of the GNEP can be found by solving a sequence of smooth NEPs.We then apply the semismooth Newton method with Armijo line search to solve latter problems and provide some results of numerical experiments to illustrate the proposed approach. 相似文献
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考虑一类随机互线性补问题的求解方法,目的是通过定义NCP函数来使正则化期望残差最小化.通过拟蒙洛包洛方法产生一系列观察值并且证得离散近似问题最小值解的聚点就是相应随机线性互补问题的期望残差最小值ERM,同时得到利用ERM到解为有界的充分条件.进一步证明ERM法能够得到具有稳定性和最小灵敏度的稳健解. 相似文献