正则化Consensus问题的收敛性证明
Convergence Proof of Regularized Consensus Problems
DOI: 10.12677/PM.2021.113049, PDF,    科研立项经费支持
作者: 刘玉洁, 毕文静, 张 炎, 俞 露, 李伟南：巢湖学院数学与统计学院，安徽 合肥
关键词: ADMM；Consensus；收敛性；ADMM； Consensus； The Convergence
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。
Abstract: 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.
文章引用：刘玉洁, 毕文静, 张炎, 俞露, 李伟南. 正则化Consensus问题的收敛性证明[J]. 理论数学, 2021, 11(3): 371-376. https://doi.org/10.12677/PM.2021.113049

参考文献

[1] Glowinski, R. and Marroco, A. (1975) Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualitéd’une classe de problèmes de Dirichlet nonlinéaires. Re-vue Francaise Dautomatique, Informatique, Recherhe Operationnelle. Analyse Numerique, 9, 41-46. [Google Scholar] [CrossRef] 
[2] Gabay, D. and Mercier, B. (1976) A Dual Algorithm for the Solution of Nonlinear Variational Problems via Finite Element Approximations. Computers & Mathematics with Applications, 2, 17-40. [Google Scholar] [CrossRef] 
[3] Lin, F., Jovanovic, M.R. and Georgiou, T.T. (2013) An ADMM Algorithm for Matrix Completion of Partially Known State Covariances. Decision & Control, 2013, 1684-1689.
[4] Wang, Y.L., Yang, J.F., Yin, W.T., et al. (2008) A New Alternating Minimization Algorithm for Total Variation Image Reconstruction. SIAM Journal on Imaging Sciences, 1, 248-272. [Google Scholar] [CrossRef] 
[5] Shen, Y. and Wang, H.Y. (2016) New Augmented Lagrangian-Based Proximal Point Algorithm for Convex Optimization with Equality Constraints. Journal Optimization Theory and Ap-plication, 171, 251-261. [Google Scholar] [CrossRef] 
[6] Boyd, S., Parikh, N., Chu, E., et al. (2011) Distributed Optimi-zation and Statistical Learning via the Alternating Direction Method of Multipliers. Found Trends Mach Learning, 3, 1-122. [Google Scholar] [CrossRef] 
[7] 申远, 孔玉倩, 纪磊. 一种新参数条件的线性化逐块交替方向乘子法[J]. 徐州工程学院学报(自然科学版), 2020, 35(2): 23-32.

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