随机广义拟变分不等式的迭代解法及应用  

Iterative Methods for Random Generalized Quasi Variational Inequalities With Applications

作　　者：王雁南 曾嘉钦 黄南京[1] WANG Yannan;ZENG Jiaqin;HUANG Nanjing(School of Mathematics,Sichuan University,Chengdu 610064,P.R.China)

机构地区：[1]四川大学数学学院,成都610064

出　　处：《应用数学和力学》2023年第11期1378-1388,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金项目(12171339);国家重点研发项目(2020YFC0832404)。

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.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 depic-ted 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.

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 

分 类 号：O177.91[理学—数学] O221.5[理学—基础数学]