非凸多分块优化部分对称正则化交替方向乘子法 简金宝¹, 刘鹏杰², 江羡珍¹1. 广西民族大学数学与物理学院应用数学与人工智能研究中心 广西混杂计算与集成电路分析重点实验室 南宁 530006;
2. 广西大学数学与信息科学学院 南宁 530004 A Partially Symmetric Regularized Alternating Direction Method of Multipliers for Nonconvex Multi-block Optimization Jin Bao JIAN¹, Peng Jie LIU², Xian Zhen JIANG¹1. College of Mathematics and Physics, Center for Applied Mathematics and Artificial Intelligence, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities, Nanning 530006, P. R. China;
2. College of Mathematics and Information Science, Guangxi University, Nanning 530004, P. R. China

摘要 图/表 参考文献 相关文章 全文: PDF(766 KB) HTML (1 KB) 输出: BibTeX | EndNote (RIS) 摘要交替方向乘子法求解两分块优化的研究已逐渐成熟和完善，但对于非凸多分块优化的研究相对较少.本文提出带线性约束的非凸多分块优化的部分对称正则化交替方向乘子法.首先，在适当的假设条件下，包括部分对称乘子修正中参数的估值区域，证明了算法的全局收敛性.其次，当增广拉格朗日函数满足Kurdyka-Lojasiewicz（KL）性质时，证明了算法的强收敛性.当KL性质关联函数具有特殊结构时，保证了算法的次线性和线性收敛率.最后，对算法进行了初步数值试验，结果表明算法的数值有效性. 服务 加入引用管理器 E-mail Alert RSS 收稿日期: 2020-06-10 MR (2010): O221 基金资助:国家自然科学基金（11771383）；广西自然科学基金（2020GXNSFDA238017，2018GXNSFFA281007） 作者简介: 简金宝,E-mail:jianjb@gxu.edu.cn;刘鹏杰,E-mail:liupengjie2019@163.com;江羡珍,E-mail:yl2811280@163.com 引用本文: 简金宝, 刘鹏杰, 江羡珍. 非凸多分块优化部分对称正则化交替方向乘子法[J]. 数学学报, 2021, 64(6): 1005-1026. Jin Bao JIAN, Peng Jie LIU, Xian Zhen JIANG. A Partially Symmetric Regularized Alternating Direction Method of Multipliers for Nonconvex Multi-block Optimization. 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