求解随机混合变分不等式问题的方差约减随机算子外推算法  

Variance-Reduction Stochastic Operator Extrapolation Algorithm for Stochastic Mixed Variational Inequalities

作　　者：杨静 龙宪军[1] YANG Jing;LONG Xianjun(College of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067

出　　处：《系统科学与数学》2023年第6期1451-1467,共17页Journal of Systems Science and Mathematical Sciences

基　　金：重庆市自然科学基金(cstc2021jcyj-msxmX0721);重庆市教育委员会科学技术研究重点项目(KJZDK201900801);经济社会应用统计重庆市重点实验室开放课题(KFJJ2022055);重庆市研究生导师团队建设项目(yds223010);重庆工商大学研究生创新型科研项目(yjscxx2023-211-70)资助课题。

摘　　要：利用方差约减策略,提出了一种新的随机算子外推算法求解随机混合变分不等式问题.所给算法每次迭代仅需计算一次期望算子的随机近似和一次广义Bregman投影.在不需要Lipschitz连续的假设下,得到了残差意义下的收敛率O(1/T),这里T表示算法得迭代次数.最后,文章将所给算法应用于求解正则化Logistic回归问题、随机网络Nash-Cournot问题以及资源调度问题.数值结果展现了文章所提算法相比已有算法的优越性.In this paper,we propose a variance-reduction stochastic operator extrapolation algorithm for solving stochastic mixed variational inequality problems.One salient feature of the algorithm is that it requires only one evaluation of the expected operator and one generalized Bregman projection calculation per iteration.Furthermore,we deduce the optimistic convergence rate O(1/T) without the assumption of Lipschitz continuity,where T denotes the number of iterations.Finally,we apply the proposed algorithm to solve regularized logistic regression problems,stochastic network game problems and resource sharing problems.The simulation results show the advantages of our algorithm comparing the existing algorithm.

关 键 词：随机混合变分不等式 算子外推 Bregman距离 资源调度问题 

分 类 号：O211.6[理学—概率论与数理统计]