正则化Consensus问题的收敛性证明  

Convergence Proof of Regularized Consensus Problems

作　　者：刘玉洁 毕文静 张炎 俞露 李伟南 

机构地区：[1]巢湖学院数学与统计学院,安徽 合肥

出　　处：《理论数学》2021年第3期371-376,共6页Pure Mathematics

摘　　要：交替方向乘子法(ADMM算法)是求解可分离凸优化问题的一种有效方法。该算法利用目标函数的可分性,将原问题拆分成若干个极小化的子问题,然后交替迭代求解。而一致性(Consensus)问题是求解大数据问题的重要的一种形式,本文提出了一种正则化的一致性问题,给出了其迭代过程,并在适当的假设下,证明了其收敛性。Alternating direction multiplier method (ADMM algorithm) is an effective method to solve sepa-rable convex optimization problems. The algorithm USES the separability of the objective function to divide the original problem into several minimization subproblems and then solve them alter-nately iteratively. Consensus is an important form of solving big data problems. In this paper, a regularized consistency problem is proposed, its iterative process is given, and its convergence is proved under appropriate assumptions.

关 键 词：ADMM CONSENSUS 收敛性 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]