随机Bregman ADMM及其在训练具有离散结构的支持向量机中的应用  

A stochastic Bregman ADMM with its application in training sparse structure SVMs

作　　者：吕袈豪 罗洪林 杨泽华 彭建文 LYU Jiahao;LUO Honglin;YANG Zehua;PENG Jianwen(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China;School of Computer and Information Science,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331 [2]重庆师范大学计算机与信息科学学院,重庆401331

出　　处：《运筹学学报》2022年第2期16-30,共15页Operations Research Transactions

基　　金：国家自然科学基金(Nos.11991024,11771064);重庆市高校创新研究群体项目(No.CXQT20014);重庆市创新领军人才项目团队(No.CQYC20210309536);重庆市科技局(No.cstc2021jcyjmsx300)。

摘　　要：针对具有多块可分结构的非凸优化问题提出了一类新的随机Bregman交替方向乘子法,在周期更新规则下,证明了该算法的渐进收敛性;在随机更新的规则下,几乎确定的渐进收敛性得以证明。数值实验结果表明,该算法可有效训练具有离散结构的支持向量机。A new stochastic Bregman multiplier alternating direction method(SB-ADMM)is proposed for non-convex optimization problems with multiple separable blocks.It is shown that the sequence produced by the S-B-ADMM under the periodic update rule converges asymptotically to a stationary solution of the Lagrangian function of the original problem.Under the random update rule,we prove the almost surely convergence of the sequence produced by the S-B-ADMM.Numerical experiments results illustrate the feasibility of the S-B-ADMM for training sparse structural support vector machines.

关 键 词：多块可分离的非凸优化问题 Bregman度量 随机交替方向乘子法 渐进收敛性 支持向量机 

分 类 号：O221.2[理学—运筹学与控制论] O224[理学—数学]