Reconstruction of electrical capacitance tomography images based on fast linearized alternating direction method of multipliers for two-phase flow system

Electrical capacitance tomography(ECT)has been applied to two-phase flow measurement in recent years.Image reconstruction algorithms play an important role in the successful applications of ECT.To solve the ill-posed and nonlinear inverse problem of ECT image reconstruction,a new ECT image reconstruction method based on fast linearized alternating direction method of multipliers(FLADMM)is proposed in this paper.On the basis of theoretical analysis of compressed sensing(CS),the data acquisition of ECT is regarded as a linear measurement process of permittivity distribution signal of pipe section.A new measurement matrix is designed and L1 regularization method is used to convert ECT inverse problem to a convex relaxation problem which contains prior knowledge.A new fast alternating direction method of multipliers which contained linearized idea is employed to minimize the objective function.Simulation data and experimental results indicate that compared with other methods,the quality and speed of reconstructed images are markedly improved.Also,the dynamic experimental results indicate that the proposed algorithm can ful fill the real-time requirement of ECT systems in the application.

Distributed MPC for Reconfigurable Architecture Systems via Alternating Direction Method of Multipliers

This paper investigates the distributed model predictive control(MPC)problem of linear systems where the network topology is changeable by the way of inserting new subsystems,disconnecting existing subsystems,or merely modifying the couplings between different subsystems.To equip live systems with a quick response ability when modifying network topology,while keeping a satisfactory dynamic performance,a novel reconfiguration control scheme based on the alternating direction method of multipliers(ADMM)is presented.In this scheme,the local controllers directly influenced by the structure realignment are redesigned in the reconfiguration control.Meanwhile,by employing the powerful ADMM algorithm,the iterative formulas for solving the reconfigured optimization problem are obtained,which significantly accelerate the computation speed and ensure a timely output of the reconfigured optimal control response.Ultimately,the presented reconfiguration scheme is applied to the level control of a benchmark four-tank plant to illustrate its effectiveness and main characteristics.

Distributed Alternating Direction Method of Multipliers for Multi-Objective Optimization

In this paper, a distributed algorithm is proposed to solve a kind of multi-objective optimization problem based on the alternating direction method of multipliers. Compared with the centralized algorithms, this algorithm does not need a central node. Therefore, it has the characteristics of low communication burden and high privacy. In addition, numerical experiments are provided to validate the effectiveness of the proposed algorithm.

Application of Linearized Alternating Direction Multiplier Method in Dictionary Learning

The Alternating Direction Multiplier Method (ADMM) is widely used in various fields, and different variables are customized in the literature for different application scenarios [1] [2] [3] [4]. Among them, the linearized alternating direction multiplier method (LADMM) has received extensive attention because of its effectiveness and ease of implementation. This paper mainly discusses the application of ADMM in dictionary learning (non-convex problem). Many numerical experiments show that to achieve higher convergence accuracy, the convergence speed of ADMM is slower, especially near the optimal solution. Therefore, we introduce the linearized alternating direction multiplier method (LADMM) to accelerate the convergence speed of ADMM. Specifically, the problem is solved by linearizing the quadratic term of the subproblem, and the convergence of the algorithm is proved. Finally, there is a brief summary of the full text.

Stochastic Accelerated Alternating Direction Method of Multipliers for Hedging Communication Noise in Combined Heat and Power Dispatch

Combined heat and power dispatch(CHPD)opens a new window for increasing operational flexibility and reducing wind power curtailment.Electric power and district heating systems are independently controlled by different system operators;therefore,a decentralized solution paradigm is necessary for CHPD,in which only minor boundary information is required to be exchanged via a communication network.However,a nonideal communication environment with noise could lead to divergence or incorrect solutions of decentralized algorithms.To bridge this gap,this paper proposes a stochastic accelerated alternating direction method of multipliers(SA-ADMM)for hedging communication noise in CHPD.This algorithm provides a general framework to address more types of constraint sets and separable objective functions than the existing stochastic ADMM.Different from the single noise sources considered in the existing stochastic approximation methods,communication noise from multiple sources is addressed in both the local calculation and the variable update stages.Case studies of two test systems validate the effectiveness and robustness of the proposed SAADMM.

A Bregman-style Partially Symmetric Alternating Direction Method of Multipliers for Nonconvex Multi-block Optimization

The alternating direction method of multipliers(ADMM)is one of the most successful and powerful methods for separable minimization optimization.Based on the idea of symmetric ADMM in two-block optimization,we add an updating formula for the Lagrange multiplier without restricting its position for multiblock one.Then,combining with the Bregman distance,in this work,a Bregman-style partially symmetric ADMM is presented for nonconvex multi-block optimization with linear constraints,and the Lagrange multiplier is updated twice with different relaxation factors in the iteration scheme.Under the suitable conditions,the global convergence,strong convergence and convergence rate of the presented method are analyzed and obtained.Finally,some preliminary numerical results are reported to support the correctness of the theoretical assertions,and these show that the presented method is numerically effective.

A New Stopping Criterion for Eckstein and Bertsekas’s Generalized Alternating Direction Method of Multipliers

In this paper,we propose a new stopping criterion for Eckstein and Bertsekas’s generalized alternating direction method of multipliers.The stopping criterion is easy to verify,and the computational cost is much less than the classical stopping criterion in the highly influential paper by Boyd et al.(Found Trends Mach Learn 3(1):1–122,2011).

A Symmetric Linearized Alternating Direction Method of Multipliers for a Class of Stochastic Optimization Problems

Alternating direction method of multipliers(ADMM)receives much attention in the recent years due to various demands from machine learning and big data related optimization.In 2013,Ouyang et al.extend the ADMM to the stochastic setting for solving some stochastic optimization problems,inspired by the structural risk minimization principle.In this paper,we consider a stochastic variant of symmetric ADMM,named symmetric stochastic linearized ADMM(SSL-ADMM).In particular,using the framework of variational inequality,we analyze the convergence properties of SSL-ADMM.Moreover,we show that,with high probability,SSL-ADMM has O((ln N)·N^(-1/2))constraint violation bound and objective error bound for convex problems,and has O((ln N)^(2)·N^(-1))constraint violation bound and objective error bound for strongly convex problems,where N is the iteration number.Symmetric ADMM can improve the algorithmic performance compared to classical ADMM,numerical experiments for statistical machine learning show that such an improvement is also present in the stochastic setting.

A Fast Symmetric Alternating Direction Method of Multipliers

In recent years,alternating direction method of multipliers(ADMM)and its variants are popular for the extensive use in image processing and statistical learning.A variant of ADMM:symmetric ADMM,which updates the Lagrange mul-tiplier twice in one iteration,is always faster whenever it converges.In this paper,combined with Nesterov’s accelerating strategy,an accelerated symmetric ADMM is proposed.We prove its O(1/k^(2))convergence rate under strongly convex condition.For the general situation,an accelerated method with a restart rule is proposed.Some preliminary numerical experiments show the efficiency of our algorithms.

面向光伏集群的配电网模型⁃数据联合驱动无功/电压控制

传统配电网的无功/电压控制(VVC)方法,难以兼顾控制决策的全局最优性与实时响应能力,分布式光伏(DPV)的分散化、高比例并网导致该矛盾日益突出。结合模型优化的寻优能力与深度强化学习的在线决策效率,提出了面向光伏(PV)集群的配电网模型-数据联合驱动VVC策略。首先,考虑日前优化调度与日内实时控制的运行特征,结合DPV集群划分,构建了配电网分布式两阶段VVC框架;然后,以系统运行网损最低为目标,建立了配电网分布式日前VVC模型,并提出了基于Nesterov加速梯度的分布式求解算法;其次,以日前决策为输入量,建立了基于部分可观马尔可夫博弈的配电网实时VVC模型,并提出了基于迭代终止惩罚函数的改进多智能体深度确定性策略梯度算法;最后,基于MATLAB/PyCharm软件平台进行了算例分析,验证了所提方法的全局趋优性以及实时响应能力,提高了PV高比例接入配电网运行的经济性和安全性。

基于分数阶全变分和低秩正则化的彩色图像去模糊方法

针对现有的彩色图像去模糊过程中存在色彩失衡、阶梯效应和伪影等现象,提出了一种基于分数阶全变分和低秩正则的图像去模糊优化方法。首先,将传统的RGB彩色图像转换到YCbCr颜色空间,利用其亮度通道特征解决色彩失衡问题;其次,利用分数阶全变分的特征消除图像恢复任务中出现的阶梯效应,并且引入加权核范数低秩正则进一步抑制伪影及噪声;最后,利用交替方向乘子法设计出高效的求解方法,通过迭代优化得到纯净图像的最优估计。对彩色图像测试的实验结果表明,所提出的方法对图像去模糊任务取得较好的视觉恢复效果,客观评价指标良好。

求解不可分离非凸非光滑问题的线性惯性ADMM算法

针对目标函数中包含耦合函数H(x,y)的非凸非光滑极小化问题,提出了一种线性惯性交替乘子方向法(Linear Inertial Alternating Direction Method of Multipliers,LIADMM)。为了方便子问题的求解,对目标函数中的耦合函数H(x,y)进行线性化处理,并在x-子问题中引入惯性效应。在适当的假设条件下,建立了算法的全局收敛性;同时引入满足Kurdyka-Lojasiewicz不等式的辅助函数,验证了算法的强收敛性。通过两个数值实验表明,引入惯性效应的算法比没有惯性效应的算法收敛性能更好。

基于压缩感知的缺失机械振动信号重构新方法

针对工业机械设备实时监测中不可控因素导致的振动信号数据缺失问题,提出一种基于自适应二次临近项交替方向乘子算法(adaptive quadratic proximity-alternating direction method of multipliers, AQ-ADMM)的压缩感知缺失信号重构方法。AQ-ADMM算法在经典交替方向乘子算法算法迭代过程中添加二次临近项,且能够自适应选取惩罚参数。首先在数据中心建立信号参考数据库用于构造初始字典,然后将K-奇异值分解(K-singular value decomposition, K-SVD)字典学习算法和AQ-ADMM算法结合重构缺失信号。对仿真信号和两种真实轴承信号数据集添加高斯白噪声后作为样本,试验结果表明当信号压缩率在50%~70%时,所提方法性能指标明显优于其它传统方法,在重构信号的同时实现了对含缺失数据机械振动信号的快速精确修复。

基于NSST与稀疏先验的遥感图像去模糊方法

针对遥感图像的模糊问题,设计一种基于非下采样剪切波变换与稀疏先验的图像复原算法.首先,利用遥感图像在非下采样剪切波分解下的高频图像的稀疏特性设置先验条件构造图像复原模型;其次,采用交替方向乘子法求解模型;再次,采用软阈值方法对高频图像进行约束处理,在低频图像进行导向滤波处理,以最大可能保留图像的细节信息;最后,将高频图像与低频图像进行重构,对重构后的图像采用卷积神经网络进行深度去噪,最终复原出清晰的图像.将该去模糊算法与H-PNP,GSR,L2TV算法进行实验对比.实验结果表明,该算法能有效去除遥感图像中的模糊和噪声,保留图像的边缘细节,客观评价指标均高于其他3种对比实验算法.

考虑碳-绿证耦合机制的电-气-热综合能源系统分布式鲁棒低碳经济调度

为了保护综合能源系统中不同运营主体的信息隐私,权衡系统运行低碳性和经济性,解决天然气网络鲁棒模型难以求解的问题,提出了考虑碳-绿证耦合机制的电-气-热综合能源系统分布式鲁棒低碳经济调度方法。考虑天然气网络和热力网络的动态特性、碳-绿证耦合机制,构建综合能源系统动态低碳经济调度模型;为了保护各网络运营商的数据隐私,根据能量耦合关系对综合能源系统解耦,建立电-气-热网络的分布式协同优化模型;在此基础上,考虑风电出力和多能负荷的不确定性,提出基于一致性交替方向乘子法的分布式鲁棒优化框架,并利用二阶锥对偶理论与交替优化方法实现含二阶锥约束和二元变量的鲁棒子问题求解。以修改的IEEE 39节点电力网络、比利时20节点天然气网络和15节点热力网络为算例进行仿真分析,验证所提方法能够在源荷不确定性条件下实现综合能源系统各网络分散自治运行,同时兼顾系统运行的低碳性和经济性。

Adaptive Linearized Alternating Direction Method of Multipliers for Non-Convex Compositely Regularized Optimization Problems

We consider a wide range of non-convex regularized minimization problems, where the non-convex regularization term is composite with a linear function engaged in sparse learning. Recent theoretical investigations have demonstrated their superiority over their convex counterparts. The computational challenge lies in the fact that the proximal mapping associated with non-convex regularization is not easily obtained due to the imposed linear composition. Fortunately, the problem structure allows one to introduce an auxiliary variable and reformulate it as an optimization problem with linear constraints, which can be solved using the Linearized Alternating Direction Method of Multipliers （LADMM）. Despite the success of LADMM in practice, it remains unknown whether LADMM is convergent in solving such non-convex compositely regularized optimizations. In this research, we first present a detailed convergence analysis of the LADMM algorithm for solving a non-convex compositely regularized optimization problem with a large class of non-convex penalties. Furthermore, we propose an Adaptive LADMM （AdaLADMM） algorithm with a line-search criterion. Experimental results on different genres of datasets validate the efficacy of the proposed algorithm.

A proximal point algorithm revisit on the alternating direction method of multipliers

The alternating direction method of multipliers(ADMM)is a benchmark for solving convex programming problems with separable objective functions and linear constraints.In the literature it has been illustrated as an application of the proximal point algorithm(PPA)to the dual problem of the model under consideration.This paper shows that ADMM can also be regarded as an application of PPA to the primal model with a customized choice of the proximal parameter.This primal illustration of ADMM is thus complemental to its dual illustration in the literature.This PPA revisit on ADMM from the primal perspective also enables us to recover the generalized ADMM proposed by Eckstein and Bertsekas easily.A worst-case O(1/t)convergence rate in ergodic sense is established for a slight extension of Eckstein and Bertsekas’s generalized ADMM.

An Alternating Direction Method of Multipliers for MCP-penalized Regression with High-dimensional Data

The minimax concave penalty （MCP） has been demonstrated theoretically and practical- ly to be effective in nonconvex penalization for variable selection and parameter estimation. In this paper, we develop an efficient alternating direction method of multipliers （ADMM） with continuation algorithm for solving the MCP-penalized least squares problem in high dimensions. Under some mild conditions, we study the convergence properties and the Karush-Kuhn-Tucker （KKT） optimality con- ditions of the proposed method. A high-dimensional BIC is developed to select the optimal tuning parameters. Simulations and a real data example are presented to illustrate the efficiency and accuracy of the proposed method.

A Survey on Some Recent Developments of Alternating Direction Method of Multipliers

Recently, alternating direction method of multipliers (ADMM) attracts much attentions from various fields and there are many variant versions tailored for differentmodels. Moreover, its theoretical studies such as rate of convergence and extensionsto nonconvex problems also achieve much progress. In this paper, we give a surveyon some recent developments of ADMM and its variants.

Decentralized Demand Management Based on Alternating Direction Method of Multipliers Algorithm for Industrial Park with CHP Units and Thermal Storage

This paper proposes a decentralized demand management approach to reduce the energy bill of industrial park and improve its economic gains.A demand management model for industrial park considering the integrated demand response of combined heat and power(CHP)units and thermal storage is firstly proposed.Specifically,by increasing the electricity outputs of CHP units during peak-load periods,not only the peak demand charge but also the energy charge can be reduced.The thermal storage can efficiently utilize the waste heat provided by CHP units and further increase the flexibility of CHP units.The heat dissipation of thermal storage,thermal delay effect,and heat losses of heat pipelines are considered for ensuring reliable solutions to the industrial park.The proposed model is formulated as a multi-period alternating current(AC)optimal power flow problem via the second-order conic programming formulation.The alternating direction method of multipliers(ADMM)algorithm is used to compute the proposed demand management model in a distributed manner,which can protect private data of all participants while achieving solutions with high quality.Numerical case studies validate the effectiveness of the proposed demand management approach in reducing peak demand charge,and the performance of the ADMM-based decentralized computation algorithm in deriving the same optimal results of demand management as the centralized approach is also validated.