一类拟单调变分不等式的惯性投影算法  

Inertial Projection Algorithms for Quasimonotone Variational Inequali ties

作　　者：杨蓝翔 陈艺 叶明露[1] Yang Lanxiang;Chen Yi;Ye Minglu(Sichuan Colleges and Universities Key Laboratory of Optimization Theory and Applications,School of Mathematics and Information,China West Normal University,Sichuan Nanchong 637009)

机构地区：[1]最优化理论与应用四川省高校重点实验室,西华师范大学数学与信息学院,四川南充637009

出　　处：《数学物理学报（A辑）》2023年第2期593-603,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金面上项目(11871059);西华师范大学培育项目(20A024)和西华师范大学校级大学生创新创业训练计划项目(cxcy2022027)。

摘　　要：2020年,Liu和Yang在Hilbert空间中提出了一种求解拟单调变分不等式的投影算法.该文介绍了一种新的惯性系数来加速Liu和Yang文中的算法,并在相同的假设条件下得到了算法的全局弱收敛性.数值实验表明适当选取参数后的惯性方法比Liu和Yang文中的算法有更少的迭代步数和计算机耗时.In 2020,Liu and Yang proposed a projection algorithm(LY for short)for solving quasimonotone variational inequality in Hilbert Space.In this paper,by taking a new inertia coefficient,we present an inertial technique to accelerate LY.Under the same assumptions,the global weak convergence of the sequence generated by this algorithm is obtained.Numerical experiments show that the new algorithm can accelerate LY from the point view of iterate number steps and the point view of CPU time cost by taking suitable parameters.

关 键 词：变分不等式 投影算法 拟单调 惯性方法 

分 类 号：O221[理学—运筹学与控制论]