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 ...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.展开更多
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 merel...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.展开更多
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 linear...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.展开更多
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 algor...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.展开更多
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...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。展开更多
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 u...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.展开更多
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 ...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).展开更多
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...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.展开更多
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 s...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.展开更多
Since the connection of small-scale wind farms to distribution networks,power grid voltage stability has been reduced with increasing wind penetration in recent years,owing to the variable reactive power consumption o...Since the connection of small-scale wind farms to distribution networks,power grid voltage stability has been reduced with increasing wind penetration in recent years,owing to the variable reactive power consumption of wind generators.In this study,a two-stage reactive power optimization method based on the alternating direction method of multipliers(ADMM)algorithm is proposed for achieving optimal reactive power dispatch in wind farm-integrated distribution systems.Unlike existing optimal reactive power control methods,the proposed method enables distributed reactive power flow optimization with a two-stage optimization structure.Furthermore,under the partition concept,the consensus protocol is not needed to solve the optimization problems.In this method,the influence of the wake effect of each wind turbine is also considered in the control design.Simulation results for a mid-voltage distribution system based on MATLAB verified the effectiveness of the proposed method.展开更多
Decoding by alternating direction method of multipliers(ADMM) is a promising linear programming decoder for low-density parity-check(LDPC) codes. In this paper, we propose a two-step scheme to lower the error floor of...Decoding by alternating direction method of multipliers(ADMM) is a promising linear programming decoder for low-density parity-check(LDPC) codes. In this paper, we propose a two-step scheme to lower the error floor of LDPC codes with ADMM penalized decoder.For the undetected errors that cannot be avoided at the decoder side, we modify the code structure slightly to eliminate low-weight code words. For the detected errors induced by small error-prone structures, we propose a post-processing method for the ADMM penalized decoder. Simulation results show that the error floor can be reduced significantly over three illustrated LDPC codes by the proposed two-step scheme.展开更多
为解决传统波束形成器在干扰位置发生扰动和导向矢量失配时,造成自适应权重的不匹配,从而导致算法性能急剧下降,甚至期望信号相消的问题,提出一种联合协方差矩阵重构和交替方向乘子法(Alternating direction method of multipliers,ADMM...为解决传统波束形成器在干扰位置发生扰动和导向矢量失配时,造成自适应权重的不匹配,从而导致算法性能急剧下降,甚至期望信号相消的问题,提出一种联合协方差矩阵重构和交替方向乘子法(Alternating direction method of multipliers,ADMM)的鲁棒波束形成方法。对此,首先基于波束形成器最大输出功率准则,设计了求解最优导向矢量的优化模型。接着,根据Capon算法空间功率谱函数,利用定义的干扰范围对协方差矩阵进行重构,以展宽零陷并增强系统抗运动干扰能力。最后,关于导向矢量的二次不等式约束问题,本质为估计导向矢量和期望导向矢量间的差异,该方法利用ADMM对该二次规划问题进行迭代求解,并在每次迭代中获得导向矢量的具体解。另外,也分析了算法的复杂度。实验结果表明:对比现有的波束形成算法,在干扰处加宽了零陷,提高了波束的抗干扰性;结合复杂度也证明了其计算速度优于现有的算法,并且能够很好地校正失配导向矢量。本方法也为求解二次不等式约束问题和提高波束形成算法性能提供了一种思路和途径。展开更多
Effective and efficient SAR image segmentation has a significant role in coastal zone interpretation. In this paper, a coastal zone segmentation model is proposed based on Potts model. By introducing edge self-adaptio...Effective and efficient SAR image segmentation has a significant role in coastal zone interpretation. In this paper, a coastal zone segmentation model is proposed based on Potts model. By introducing edge self-adaption parameter and modifying noisy data term, the proposed variational model provides a good solution for the coastal zone SAR image with common characteristics of inherent speckle noise and complicated geometrical details. However, the proposed model is difficult to solve due to to its nonlinear, non-convex and non-smooth characteristics. Followed by curve evolution theory and operator splitting method, the minimization problem is reformulated as a constrained minimization problem. A fast alternating minimization iterative scheme is designed to implement coastal zone segmentation. Finally, various two-stage and multiphase experimental results illustrate the advantage of the proposed segmentation model, and indicate the high computation efficiency of designed numerical approximation algorithm.展开更多
实时电价是智能电网需求侧管理的有效方法,对于维持电力供需平衡、削峰填谷至关重要。为提高实时电价模型的低碳经济性和精确性,在充分考虑用户与供电侧双方利益前提下提出碳交易机制,并根据新能源的发电特性构建风光出力不确定模型,建...实时电价是智能电网需求侧管理的有效方法,对于维持电力供需平衡、削峰填谷至关重要。为提高实时电价模型的低碳经济性和精确性,在充分考虑用户与供电侧双方利益前提下提出碳交易机制,并根据新能源的发电特性构建风光出力不确定模型,建立以用户总效用最大、供电侧成本最小为目标的社会福利最大化实时电价模型。提出基于改进交替方向乘子法(alternating direction method of multiplier, ADMM),即高斯回代交替方向乘子法(ADMM with Gaussian back substitution, ADMM-GBS)的分布式优化调度方法,通过将不确定模型转化为确定模型求解。仿真结果表明,所提实时电价策略能够提升社会福利,验证了模型和算法的有效性。展开更多
基金Supported by the National Natural Science Foundation of China(61203021)the Key Science and Technology Program of Liaoning Province(2011216011)+1 种基金the Natural Science Foundation of Liaoning Province(2013020024)the Program for Liaoning Excellent Talents in Universities(LJQ2015061)
文摘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.
基金the National Natural Science Foundation of China(61833012,61773162,61590924)the Natural Science Foundation of Shanghai(18ZR1420000)。
文摘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.
文摘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.
文摘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.
文摘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。
基金supported by the National Natural Science Foundation of China (No.12171106)the Natural Science Foundation of Guangxi Province (No.2020GXNSFDA238017)。
文摘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.
文摘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).
基金supported by the Key-Area Research and Development Program of Guangdong Province under Grant 2020B010166004the National Natural Science Foundation of China under Grant 52177086+2 种基金the Guangdong Basic and Applied Basic Research Foundation under Grant 2019A1515011408the Science and Technology Program of Guangzhou under Grant 201904010215the Talent Recruitment Project of Guangdong under Grant 2017GC010467.
文摘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.
基金Supported by National Natural Science Foundation of China (61662036)。
文摘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.
基金support of The National Key Research and Development Program of China(Basic Research Class)(No.2017YFB0903000)the National Natural Science Foundation of China(No.U1909201)。
文摘Since the connection of small-scale wind farms to distribution networks,power grid voltage stability has been reduced with increasing wind penetration in recent years,owing to the variable reactive power consumption of wind generators.In this study,a two-stage reactive power optimization method based on the alternating direction method of multipliers(ADMM)algorithm is proposed for achieving optimal reactive power dispatch in wind farm-integrated distribution systems.Unlike existing optimal reactive power control methods,the proposed method enables distributed reactive power flow optimization with a two-stage optimization structure.Furthermore,under the partition concept,the consensus protocol is not needed to solve the optimization problems.In this method,the influence of the wake effect of each wind turbine is also considered in the control design.Simulation results for a mid-voltage distribution system based on MATLAB verified the effectiveness of the proposed method.
基金supported in part by National Nature Science Foundation of China under Grant No.61471286,No.61271004the Fundamental Research Funds for the Central Universitiesthe open research fund of Key Laboratory of Information Coding and Transmission,Southwest Jiaotong University(No.2010-03)
文摘Decoding by alternating direction method of multipliers(ADMM) is a promising linear programming decoder for low-density parity-check(LDPC) codes. In this paper, we propose a two-step scheme to lower the error floor of LDPC codes with ADMM penalized decoder.For the undetected errors that cannot be avoided at the decoder side, we modify the code structure slightly to eliminate low-weight code words. For the detected errors induced by small error-prone structures, we propose a post-processing method for the ADMM penalized decoder. Simulation results show that the error floor can be reduced significantly over three illustrated LDPC codes by the proposed two-step scheme.
文摘为解决传统波束形成器在干扰位置发生扰动和导向矢量失配时,造成自适应权重的不匹配,从而导致算法性能急剧下降,甚至期望信号相消的问题,提出一种联合协方差矩阵重构和交替方向乘子法(Alternating direction method of multipliers,ADMM)的鲁棒波束形成方法。对此,首先基于波束形成器最大输出功率准则,设计了求解最优导向矢量的优化模型。接着,根据Capon算法空间功率谱函数,利用定义的干扰范围对协方差矩阵进行重构,以展宽零陷并增强系统抗运动干扰能力。最后,关于导向矢量的二次不等式约束问题,本质为估计导向矢量和期望导向矢量间的差异,该方法利用ADMM对该二次规划问题进行迭代求解,并在每次迭代中获得导向矢量的具体解。另外,也分析了算法的复杂度。实验结果表明:对比现有的波束形成算法,在干扰处加宽了零陷,提高了波束的抗干扰性;结合复杂度也证明了其计算速度优于现有的算法,并且能够很好地校正失配导向矢量。本方法也为求解二次不等式约束问题和提高波束形成算法性能提供了一种思路和途径。
基金supported by the China Postdoctoral Science Foundation under Grant No.2015M571993the Shandong Provincial Natural Science Foundation,China under Grant No.ZR2017MD004+1 种基金the National Natural Science Foundation of China under Grant No.61602269Qingdao Postdoctoral Application Research Funded Project
文摘Effective and efficient SAR image segmentation has a significant role in coastal zone interpretation. In this paper, a coastal zone segmentation model is proposed based on Potts model. By introducing edge self-adaption parameter and modifying noisy data term, the proposed variational model provides a good solution for the coastal zone SAR image with common characteristics of inherent speckle noise and complicated geometrical details. However, the proposed model is difficult to solve due to to its nonlinear, non-convex and non-smooth characteristics. Followed by curve evolution theory and operator splitting method, the minimization problem is reformulated as a constrained minimization problem. A fast alternating minimization iterative scheme is designed to implement coastal zone segmentation. Finally, various two-stage and multiphase experimental results illustrate the advantage of the proposed segmentation model, and indicate the high computation efficiency of designed numerical approximation algorithm.
文摘太赫兹波具有频率高、波长短的特点,因此相对于传统的工作在微波波段的合成孔径雷达(Synthetic Aperture Radar,SAR),太赫兹SAR具有高成像分辨率,并在视频SAR、慢动目标检测等方面具有显著的优势。但与此同时,太赫兹SAR也对雷达平台的高频振动非常敏感。对于机载太赫兹SAR,由于气流和载机自身飞行特性的影响,载机存在高频振动,会造成回波信号的相位误差,并使成像结果出现鬼影目标和散焦现象,严重恶化成像质量。为了实现聚焦成像,需要对机载太赫兹SAR的进行高频振动补偿。不同于现有的将高频振动建模为多个简谐运动之和形式的算法,本文提出了一种基于交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)的高频误差补偿方法,无须对高频振动进行建模,可以补偿更复杂的高频振动相位误差。首先通过对接收到的回波信号使用方位向快速傅里叶变换(Fast Fourier Transform,FFT)得到粗聚焦的图像,然后将振动补偿问题转化为图像的l1范数最小化问题,引入辅助变量构造目标函数并使用ADMM算法求解。在ADMM算法迭代过程的每次循环中,利用图像熵最小化准则对相位误差进行更新。最后利用估计得到的相位误差构造相位补偿信号,用于补偿太赫兹SAR回波信号的相位误差。对点目标和分布式场景的仿真实验结果验证了该方法的有效性,且在低信噪比条件下也能获得聚焦良好的图像。
文摘实时电价是智能电网需求侧管理的有效方法,对于维持电力供需平衡、削峰填谷至关重要。为提高实时电价模型的低碳经济性和精确性,在充分考虑用户与供电侧双方利益前提下提出碳交易机制,并根据新能源的发电特性构建风光出力不确定模型,建立以用户总效用最大、供电侧成本最小为目标的社会福利最大化实时电价模型。提出基于改进交替方向乘子法(alternating direction method of multiplier, ADMM),即高斯回代交替方向乘子法(ADMM with Gaussian back substitution, ADMM-GBS)的分布式优化调度方法,通过将不确定模型转化为确定模型求解。仿真结果表明,所提实时电价策略能够提升社会福利,验证了模型和算法的有效性。