Iterative Methods for Random Generalized Quasi Variational Inequalities With Applications
edited-by
edited-by
(Contributed by HUANG Nanjing, M. AMM Ediorial Board)-
摘要: 为了获得Hilbert空间中一类随机广义拟变分不等式的迭代解法, 证明了点到由具闭(凸)值的随机集值映射所刻画的变约束集上的投影算子的可测性.利用该可测性结果和可测选择定理, 构造了求解随机广义拟变分不等式的随机迭代算法.在单调性及Lipschitz连续性条件下, 获得了由算法生成的随机序列的收敛性.作为应用, 给出了随机广义Nash博弈和随机Walrasian均衡问题的一些刻画性结果.
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关键词:
- 随机拟变分不等式 /
- 随机迭代算法 /
- 收敛性 /
- 随机Nash均衡 /
- 随机Walrasian均衡
Abstract: To obtain the iterative methods for solving a class of random generalized quasi variational inequalities (RGQVIs) in the Hilbert spaces, the measurability of the projection operators on varying-constraint sets depicted by the mapping from points to random-value sets with closed (convex) values, was proved. Moreover, the random iterative algorithm was proposed for solving RGQVIs, and the convergence of the random sequences generated with the random iterative algorithm was obtained under some suitable conditions of monotony and Lipschitz continuity. Finally, 2 applications were given with depicting results of the random generalized Nash games and random Walrasian equilibrium problems, respectively.-
Key words:
- random quasi variational inequality /
- random iterative algorithm /
- convergence /
- random Nash equilibrium /
- random Walrasian equilibrium
edited-byedited-by1) (我刊编委黄南京来稿) -
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