一种基于预估-校正格式的扩展型ADMM算法  

An Extended ADMM Algorithm Based on the Prediction-correction Framework

作　　者：高前明 费翔 GAO Qian-ming;FEI Xiang(Department of Foundational Course,Jiangsu Vocational College of Finance and Technology,Huai'an Jiangsu 223003,China;School of Mathematics and Statistics,Anhui Normal University,Wuhu Anhui 241000,China)

机构地区：[1]江苏财经职业技术学院基础教学部,江苏淮安223003 [2]安徽师范大学数学与统计学院,安徽芜湖241000

出　　处：《淮阴师范学院学报（自然科学版）》2024年第3期210-216,共7页Journal of Huaiyin Teachers College(Natural Science Edition)

基　　金：大学生创新创业训练计划项目(202210323013Z)。

摘　　要：为了降低大规模线性约束可分凸优化问题的维度,加快问题的求解速度,提出一种基于预估-校正格式的扩展型邻近对称交替方向乘子法(ADMM)-EPSADMM算法.该算法在对n-1个子问题引入带参数临近项的基础上,使用新的校正矩阵对每次迭代更新的序列进行校正,松弛了校正步长的取值范围.数值实验表明,EPSADMM算法比其他基于ADMM的算法有更快的收敛速度.In order to reduce the dimension of large-scale linear constraints separable convex optimization problem,improve the convergence speed of the problem,an extended symmetric alternating direction multiplier method(ADMM)with adjacent term is proposed based on the prediction-correction framework(EPSADMM).The algorithm introduces the adjacent term with parameter into the each sub-problem and corrects the sequence by using the new correction matrix,and relaxes the range of correction step.Numerical experiments show that the EPSADMM algorithm has faster convergence rates than other algorithms based on ADMM.

关 键 词：可分凸优化 交替方向乘子法 预估-校正格式 变分不等式 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]