| 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 |
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| 引用本文： | 吕袈豪,罗洪林,杨泽华,彭建文.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[J].运筹学学报,2021,26(2):16-30. |
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| 作者姓名： | 吕袈豪 罗洪林 杨泽华 彭建文 |
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| 作者单位： | 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 |
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| 基金项目： | 国家自然科学基金(11991024);国家自然科学基金(11771064);重庆市高校创新研究群体项目(CXQT20014);重庆市创新领军人才项目团队(CQYC20210309536);重庆市科技局(cstc2021jcyj-msx300) |
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| 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。
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| 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 |
| 收稿时间： | 2021-03-08 |
A stochastic Bregman ADMM with its application in training sparse structure SVMs |
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| Jiahao LYU,Honglin LUO,Zehua YANG,Jianwen PENG.A stochastic Bregman ADMM with its application in training sparse structure SVMs[J].OR Transactions,2021,26(2):16-30. |
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| Authors: | Jiahao LYU Honglin LUO Zehua YANG Jianwen PENG |
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| Institution: | 1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China;2. School of Computer and Information Science, Chongqing Normal University, Chongqing 401331, China |
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| Abstract: | A new stochastic Bregman multiplier alternating direction method (S-B-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. |
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| Keywords: | non-convex optimization problems with multiple separable blocks Bregman divergence stochastic ADMM asymptotic convergence support vector machine |
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