一类带线性约束的变分不等式的预测校正方法的收敛率分析  

Convergence Rate Analysis of Prediction Correction Methods for a Class of Variational Inequalities with Linear Constraints

作　　者：葛志利 谭志聪 徐莹莹 张欣 Ge Zhili;Tan Zhicong;Xu Yingying;Zhang Xin(School of Mathematics and Information Science,Nanjing Normal University of Special Education,Nanjing 210048,China;School of Information Science and Engineering,Southeast University,Nanjing 211189,China;School of Arts and Science,Suqian University,Suqian 223800,China)

机构地区：[1]南京特殊教育师范学院数学与信息科学学院,江苏南京210038 [2]东南大学信息科学与工程学院,江苏南京211189 [3]宿迁学院文理学院,江苏宿迁223800

出　　处：《南京师大学报（自然科学版）》2024年第3期1-7,共7页Journal of Nanjing Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(120081);江苏省青蓝工程项目、宿迁市科技计划资助项目(M202206);宿迁学院高级别纵向科研培育项目.

摘　　要：考虑一类带线性约束的变分不等式问题:寻找x^(*)∈Ω满足F(x^(*))^(T)(x-x^(*))≥0,■x∈Ω,其中Ω={x∈R^(n)|Ax≤b,x∈K},A∈R^(m×n),b∈R^(m),K是R^(n)上的一个简单的非空闭凸子集,F是R^(n)到R^(n)的连续未知算子且满足强单调.对此类问题,本文研究了一种新的预测校正方法.根据已有的收敛性结果,利用误差界条件进一步分析了该方法的线性收敛性.最后,通过交通均衡问题中两个带线性约束例子的数值结果展示了算法的有效性.This paper considers a class of variational inequalities with linear constraints:finding x^(*)∈Ω,such that F(x*)^(T)(x-x*)≥0,x∈Ω,whereΩ={x∈R^(n)|Ax≤b,x∈K},A∈R^(m×n),b∈R^(m),K is a simple nonempty closed convex subset of R^(n),F is a continuous unknown mapping from R^(n) to R^(n),and satisfies the strong monotonicity.We study a new prediction correction method for this class of problems.Based on the previous convergence results,we further analyze the linear convergence by using the error bound condition.Finally,two numerical results in traffic equilibrium problems with linear constraints demonstrate the effectiveness of the algorithm.

关 键 词：线性约束 变分不等式 全局线性收敛性 预测校正方法 

分 类 号：O221.4[理学—运筹学与控制论]