The alternating direction method of multipliers (ADMM) algorithm has been widely employed for distributed machine learning tasks. However, it suffers from several limitations, e.g., a relative low convergence speed, and an expensive time cost. To this end, in this paper, a novel method, namely the group-based ADMM (GADMM), is proposed for distributed linear classification. In particular, to accelerate the convergence speed and improve global consensus, a group layer is first utilized in GADMM to divide all the slave nodes into several groups. Then, all the local variables (from the slave nodes) are gathered in the group layer to generate different group variables. Finally, by using a weighted average method, the group variables are coordinated to update the global variable (from the master node) until the solution of the global problem is reached. According to the theoretical analysis, we found that: 1) GADMM can mathematically converge at the rate , where is the number of outer iterations and 2) by using the grouping methods, GADMM can improve the convergence speed compared with the distributed ADMM framework without grouping methods. Moreover, we systematically evaluate GADMM on four publicly available LIBSVM datasets. Compared with disADMM and stochastic dual coordinate ascent with alternating direction method of multipliers-ADMM, for distributed classification, GADMM is able to reduce the number of outer iterations, which leads to faster convergence speed and better global consensus. In particular, the statistical significance test has been experimentally conducted and the results validate that GADMM can significantly save up to 30% of the total time cost (with less than 0.6% accuracy loss) compared with disADMM on large-scale datasets, e.g., webspam and epsilon.

For some nonlinear dynamic systems with uncertainties or disturbances, neural networks can perform intelligent cognition and simulation on them, achieve a good system description, and further realize intelligent control. Aiming at the ethylene rectification process, in order to avoid the time delay of complex rectification process modeling and large-scale process simulation software interface program, and to improve the simulation operation speed, the optimization model combined with the learning function of the neural network is used for the simulation calculation of the rectification process. It can meet the time and accuracy requirements of online optimization. This article outlines several commonly used neural network algorithms and their related applications in ethylene distillation, aiming to provide reference for the development and innovation of industry technology.

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In recent years, with the explosive growth of the data, a wide range of data in Cyber-Physical-Social Systems (CPSS) are generated and collected as big data. Cloud computing have been widely-used as the supporting computation infrastructure, which makes big data analysis gaining much attention from IT industry and academia. Moreover, the data often are distributed and stored in different computation resources in many big data applications. Therefore, distributed computing and optimization has been developed for solving big data problems in cloud computing. time efficiency is the significant bottleneck in the performance of distributed optimization algorithms. In this paper, we propose a novel fast distributed algorithm via Alternating Direction Method of Multipliers with Adaptive Local Update (ADMM-ALU), that uses an efficient adaptive local update strategy to accelerate the speed of convergence by automatically determining the number of inner iterations of local update in each outer iteration (communication round). In particular, our method applies the optimality conditions and the magnitudes of residuals of ADMM to freely steer the trade-off between communication and local computation. Empirically, the performance of our method is tested on several benchmark datasets, and the experimental results show that compared to various versions of ADMM algorithms, our method converges faster, and could be a highly effective and efficient algorithm for practical use in big data applications. INDEX TERMS Cloud computing, big data, distributed computing, alternating direction method of multipliers.