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一类自适应广义交替方向乘子法

本站小编 Free考研考试/2021-12-27

姜帆, 刘雅梅, 蔡邢菊
南京师范大学数学科学学院, 南京 210023
收稿日期:2018-01-13出版日期:2018-12-15发布日期:2018-11-20


基金资助:国家自然科学基金青年项目(11401315),国家自然科学基金项目(11571178).


A SELF-ADAPTIVE GENERALIZED ALTERNATING DIRECTION METHOD OF MULTIPLIERS

Jiang Fan, Liu Yamei, Cai Xingju
School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
Received:2018-01-13Online:2018-12-15Published:2018-11-20







摘要



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广义交替方向乘子法是求解凸优化问题的有效算法.当实际问题中子问题难以求解时,可以采用在子问题中添加邻近项的方法处理,邻近矩阵正定时,算法收敛,然而这也会使迭代步长较小.最新研究表明,邻近矩阵可以有一定的不正定性.本文在基于不定邻近项的广义交替方向乘子法框架下,提出一种自适应的广义交替方向乘子法,动态地选择邻近矩阵,增大迭代步长.在一些较弱的假设下,证明了算法的全局收敛性.我们进行一些初等数值实验,验证了算法的有效性.
MR(2010)主题分类:
90C25
90C30
65K05

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