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正则化Consensus问题的收敛性证明
Convergence Proof of Regularized Consensus Problems

DOI: 10.12677/PM.2021.113049, PP. 371-376

Keywords: ADMM，Consensus，收敛性
ADMM, Consensus, The Convergence

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Abstract:

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.

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