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一类非凸优化问题广义交替方向法的收敛性

王欣 郭科

王欣, 郭科. 一类非凸优化问题广义交替方向法的收敛性[J]. 应用数学和力学, 2018, 39(12): 1410-1425. doi: 10.21656/1000-0887.380334
引用本文: 王欣, 郭科. 一类非凸优化问题广义交替方向法的收敛性[J]. 应用数学和力学, 2018, 39(12): 1410-1425. doi: 10.21656/1000-0887.380334
WANG Xin, GUO Ke. Convergence of the Generalized Alternating Direction Method of Multipliers for a Class of Nonconvex Optimization Problems[J]. Applied Mathematics and Mechanics, 2018, 39(12): 1410-1425. doi: 10.21656/1000-0887.380334
Citation: WANG Xin, GUO Ke. Convergence of the Generalized Alternating Direction Method of Multipliers for a Class of Nonconvex Optimization Problems[J]. Applied Mathematics and Mechanics, 2018, 39(12): 1410-1425. doi: 10.21656/1000-0887.380334

一类非凸优化问题广义交替方向法的收敛性

doi: 10.21656/1000-0887.380334
基金项目: 国家自然科学基金(11571178;11801455);2018年国家级大学生创新创业训练计划项目(201810638002)
详细信息
    作者简介:

    王欣(1991—),女,硕士生(E-mail: wangxinwatermelon@163.com);郭科(1989—),男,讲师,博士(通讯作者. E-mail: keguo2014@126.com).

  • 中图分类号: O221.2;O224

Convergence of the Generalized Alternating Direction Method of Multipliers for a Class of Nonconvex Optimization Problems

Funds: The National Natural Science Foundation of China(11571178; 11801455)
  • 摘要: 考虑利用广义交替方向法(GADMM)求解线性约束两个函数和的最小值问题,其中一个函数为凸函数,另一个函数可以表示为两个凸函数的差.对GADMM的每一个子问题,采用两个凸函数之差算法中的线性化技术来处理.通过假定相应函数满足Kurdyka-ojasiewicz不等式,当增广Lagrange(拉格朗日)函数的罚参数充分大时,证明了GADMM所产生的迭代序列收敛到增广Lagrange函数的稳定点.最后,给出了该算法的收敛速度分析.
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出版历程
  • 收稿日期:  2017-12-27
  • 修回日期:  2018-10-18
  • 刊出日期:  2018-12-01

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