郭科,王欣.广义乘子交替方向法求解线性约束不可分非凸优化问题的收敛性[J].数学研究及应用,2018,38(5):523~540
广义乘子交替方向法求解线性约束不可分非凸优化问题的收敛性
Convergence of Generalized Alternating Direction Method of Multipliers for Nonseparable Nonconvex Objective with Linear Constraints
投稿时间:2017-09-03  修订日期:2018-06-05
DOI:10.3770/j.issn:2095-2651.2018.05.010
中文关键词:  
英文关键词:generalized alternating direction method of multipliers  Kurdyka-{\L}ojasiewicz inequality  nonconvex optimization
基金项目:
作者单位
郭科 西华师范大学数学与信息学院, 四川 南充 637002 
王欣 西华师范大学数学与信息学院, 四川 南充 637002 
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中文摘要:
      
英文摘要:
      In this paper, we consider the convergence of the generalized alternating direction method of multipliers (GADMM) for solving linearly constrained nonconvex minimization model whose objective contains coupled functions. Under the assumption that the augmented Lagrangian function satisfies the Kurdyka-{\L}ojasiewicz inequality, we prove that the sequence generated by the GADMM converges to a critical point of the augmented Lagrangian function when the penalty parameter in the augmented Lagrangian function is sufficiently large. Moreover, we also present some sufficient conditions guaranteeing the sublinear and linear rate of convergence of the algorithm.
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