The task of dividing corrupted-data into their respective subspaces can be well illustrated,both theoretically and numerically,by recovering low-rank and sparse-column components of a given matrix.Generally,it can be ...The task of dividing corrupted-data into their respective subspaces can be well illustrated,both theoretically and numerically,by recovering low-rank and sparse-column components of a given matrix.Generally,it can be characterized as a matrix and a 2,1-norm involved convex minimization problem.However,solving the resulting problem is full of challenges due to the non-smoothness of the objective function.One of the earliest solvers is an 3-block alternating direction method of multipliers(ADMM)which updates each variable in a Gauss-Seidel manner.In this paper,we present three variants of ADMM for the 3-block separable minimization problem.More preciously,whenever one variable is derived,the resulting problems can be regarded as a convex minimization with 2 blocks,and can be solved immediately using the standard ADMM.If the inner iteration loops only once,the iterative scheme reduces to the ADMM with updates in a Gauss-Seidel manner.If the solution from the inner iteration is assumed to be exact,the convergence can be deduced easily in the literature.The performance comparisons with a couple of recently designed solvers illustrate that the proposed methods are effective and competitive.展开更多
A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first ...A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.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
针对智能反射面(reconfigurable intelligent surface,RIS)辅助的毫米波通信系统中传统信道估计方案导频开销过高、计算复杂度较大的问题,提出了一种基于多用户联合场景的交替方向乘子法(alternating direction method of multipliers,A...针对智能反射面(reconfigurable intelligent surface,RIS)辅助的毫米波通信系统中传统信道估计方案导频开销过高、计算复杂度较大的问题,提出了一种基于多用户联合场景的交替方向乘子法(alternating direction method of multipliers,ADMM)信道估计方案。首先,利用不同用户级联信道存在公共BS-RIS部分,估计出用户信号的公共子空间并进行投影,有效减弱了噪声的影响。其次,考虑多用户级联信道的相关性和稀疏性,构建了稀疏级联信道矩阵和公共缩放因子矩阵的优化问题。对于该非凸联合优化问题,采用ADMM算法,交替优化估计稀疏矩阵和公共缩放因子矩阵。仿真结果表明,与现有方法相比,提出的基于多用户联合的ADMM信道估计方案导频开销将减少约50%。展开更多
为研究完全去中心化的点对点(peer-to-peer,P2P)能源市场中产消者的最优清算问题,重点解决产消者内部的协作和在P2P市场中实现社会福利最大化的挑战,采用了一种新的平行、分布式的交替方向乘子法(alternating direction method of multi...为研究完全去中心化的点对点(peer-to-peer,P2P)能源市场中产消者的最优清算问题,重点解决产消者内部的协作和在P2P市场中实现社会福利最大化的挑战,采用了一种新的平行、分布式的交替方向乘子法(alternating direction method of multipliers,ADMM),推导出P2P市场的交易机制。该方法考虑每个产消者的效用函数,并引入分布式发电机(distributed generator,DG)和电能存储系统(battery energy storage system,BESS)。算法中每个产消者通过迭代与其相邻的产消者同步交换少量信息,并优化以满足不同的需求。通过对6-peers系统的数值验证,证明了所提出方法的有效性。与基于池的交易机制相比,完全去中心化的P2P问题在单位时间内交易电量提升了160%,社会福利从-9.47元增加到32.43元。展开更多
针对压缩感知下与字典学习和交替方向乘子算法(alternating direction method of multipliers,ADMM)密切相关方法存在的问题,研究并提出了一种在压缩感知理论下采用字典学习和ADMM重建地震数据的方法。首先对不完整地震数据进行字典学习...针对压缩感知下与字典学习和交替方向乘子算法(alternating direction method of multipliers,ADMM)密切相关方法存在的问题,研究并提出了一种在压缩感知理论下采用字典学习和ADMM重建地震数据的方法。首先对不完整地震数据进行字典学习,使其稀疏地表示,再根据地震道的缺失情况设计合理的采样矩阵,最后对建立的L1范数约束模型采用ADMM进行求解得到重建后的地震数据。建立了压缩感知下基于字典学习和ADMM的地震数据插值技术流程。正演模拟数据和实际数据的重建实验结果表明:与压缩感知理论下采用固定基的重建方法相比,字典学习能够自适应地对地震数据进行更优的稀疏表示。与常用的curvelet等重建算法相比,采用ADMM能够更加精确地重建地震数据。与固定基和正交匹配追踪(orthogonal matching pursuit,OMP)相比,在压缩感知理论下采用字典学习和ADMM重建的地震数据有更高的信噪比。展开更多
电网中的不同电力公司所管辖子系统具有相互独立且互联的特点,各子系统之间的互联给电网的分布式计算带来一定挑战,如何实现大系统的分布式计算备受关注。提出基于交替方向乘子法(alternating directionmethod of multipliers,ADMM)的...电网中的不同电力公司所管辖子系统具有相互独立且互联的特点,各子系统之间的互联给电网的分布式计算带来一定挑战,如何实现大系统的分布式计算备受关注。提出基于交替方向乘子法(alternating directionmethod of multipliers,ADMM)的含风电场系统分布式直流最优潮流(direct current optimal power flow,DC-OPF)计算模型,该模型考虑风电并网对系统分布式DC-OPF的影响,采用分解协调法实现系统的分区过程,通过引入全局变量处理边界节点问题,在信息传递过程中无需中心处理系统,只在相邻子区域之间进行复制边界节点的信息传递以减少信息通信量,实现系统的全分布式DC-OPF计算。以6节点系统、IEEE-39节点系统分析全局变量的个数对迭代收敛的影响,并讨论风电并网对优化收敛的影响,最后通过仿真验证该文所提模型的准确性和有效性。展开更多
通过增加伪码字的代价,基于交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)的惩罚译码方法可以改善低密度奇偶校验(Low-Density Parity-Check,LDPC)码低信噪比区域的译码性能,同时具有低的译码复杂度.而减少ADMM惩...通过增加伪码字的代价,基于交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)的惩罚译码方法可以改善低密度奇偶校验(Low-Density Parity-Check,LDPC)码低信噪比区域的译码性能,同时具有低的译码复杂度.而减少ADMM惩罚译码的欧几里德投影次数、选择合适的消息调度策略和设计有效的罚函数是提高ADMM惩罚译码速度的三种重要方法.为了进一步提高ADMM惩罚译码速度,通过利用Wei等人提出的方法来减少欧几里德投影的次数,本文设计了基于I-l1-PF罚函数的水平分层调度与垂直分层调度策略的两种LDPC码ADMM惩罚译码方法.仿真实验表明,与现有ADMM惩罚译码方法相比较,所设计的译码方法不仅具有较好的译码性能,而且能够显著降低LDPC码译码的平均迭代次数和平均译码时间.展开更多
经典的非参数谱分析方法使用滑动窗口来捕捉大多数时间序列的频谱特性,然而这种方法不能很好地应用在时间序列的时频谱是时间连续的信号上.对于一些其时频谱满足时间连续频率稀疏的非平稳信号,提出了一种利用部分平行交替方向乘子法(Alt...经典的非参数谱分析方法使用滑动窗口来捕捉大多数时间序列的频谱特性,然而这种方法不能很好地应用在时间序列的时频谱是时间连续的信号上.对于一些其时频谱满足时间连续频率稀疏的非平稳信号,提出了一种利用部分平行交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)求解谱寻求问题用于此类信号的时频分析方法.对一段加噪声的仿真信号和一段EEG(脑电)信号使用提出的方法进行时频分析.仿真结果表明:与短时傅里叶的分析方法相比,提出的方法不仅提高了时频谱的频率分辨率和时间分辨率,还有效抑制了噪声.最后从ADMM算法停止准则的角度说明了算法的收敛.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11971149,11871381)Natural Science Foundation of Henan Province for Youth(Grant No.202300410146)。
文摘The task of dividing corrupted-data into their respective subspaces can be well illustrated,both theoretically and numerically,by recovering low-rank and sparse-column components of a given matrix.Generally,it can be characterized as a matrix and a 2,1-norm involved convex minimization problem.However,solving the resulting problem is full of challenges due to the non-smoothness of the objective function.One of the earliest solvers is an 3-block alternating direction method of multipliers(ADMM)which updates each variable in a Gauss-Seidel manner.In this paper,we present three variants of ADMM for the 3-block separable minimization problem.More preciously,whenever one variable is derived,the resulting problems can be regarded as a convex minimization with 2 blocks,and can be solved immediately using the standard ADMM.If the inner iteration loops only once,the iterative scheme reduces to the ADMM with updates in a Gauss-Seidel manner.If the solution from the inner iteration is assumed to be exact,the convergence can be deduced easily in the literature.The performance comparisons with a couple of recently designed solvers illustrate that the proposed methods are effective and competitive.
文摘A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.
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.
文摘针对智能反射面(reconfigurable intelligent surface,RIS)辅助的毫米波通信系统中传统信道估计方案导频开销过高、计算复杂度较大的问题,提出了一种基于多用户联合场景的交替方向乘子法(alternating direction method of multipliers,ADMM)信道估计方案。首先,利用不同用户级联信道存在公共BS-RIS部分,估计出用户信号的公共子空间并进行投影,有效减弱了噪声的影响。其次,考虑多用户级联信道的相关性和稀疏性,构建了稀疏级联信道矩阵和公共缩放因子矩阵的优化问题。对于该非凸联合优化问题,采用ADMM算法,交替优化估计稀疏矩阵和公共缩放因子矩阵。仿真结果表明,与现有方法相比,提出的基于多用户联合的ADMM信道估计方案导频开销将减少约50%。
文摘为研究完全去中心化的点对点(peer-to-peer,P2P)能源市场中产消者的最优清算问题,重点解决产消者内部的协作和在P2P市场中实现社会福利最大化的挑战,采用了一种新的平行、分布式的交替方向乘子法(alternating direction method of multipliers,ADMM),推导出P2P市场的交易机制。该方法考虑每个产消者的效用函数,并引入分布式发电机(distributed generator,DG)和电能存储系统(battery energy storage system,BESS)。算法中每个产消者通过迭代与其相邻的产消者同步交换少量信息,并优化以满足不同的需求。通过对6-peers系统的数值验证,证明了所提出方法的有效性。与基于池的交易机制相比,完全去中心化的P2P问题在单位时间内交易电量提升了160%,社会福利从-9.47元增加到32.43元。
文摘针对压缩感知下与字典学习和交替方向乘子算法(alternating direction method of multipliers,ADMM)密切相关方法存在的问题,研究并提出了一种在压缩感知理论下采用字典学习和ADMM重建地震数据的方法。首先对不完整地震数据进行字典学习,使其稀疏地表示,再根据地震道的缺失情况设计合理的采样矩阵,最后对建立的L1范数约束模型采用ADMM进行求解得到重建后的地震数据。建立了压缩感知下基于字典学习和ADMM的地震数据插值技术流程。正演模拟数据和实际数据的重建实验结果表明:与压缩感知理论下采用固定基的重建方法相比,字典学习能够自适应地对地震数据进行更优的稀疏表示。与常用的curvelet等重建算法相比,采用ADMM能够更加精确地重建地震数据。与固定基和正交匹配追踪(orthogonal matching pursuit,OMP)相比,在压缩感知理论下采用字典学习和ADMM重建的地震数据有更高的信噪比。
文摘电网中的不同电力公司所管辖子系统具有相互独立且互联的特点,各子系统之间的互联给电网的分布式计算带来一定挑战,如何实现大系统的分布式计算备受关注。提出基于交替方向乘子法(alternating directionmethod of multipliers,ADMM)的含风电场系统分布式直流最优潮流(direct current optimal power flow,DC-OPF)计算模型,该模型考虑风电并网对系统分布式DC-OPF的影响,采用分解协调法实现系统的分区过程,通过引入全局变量处理边界节点问题,在信息传递过程中无需中心处理系统,只在相邻子区域之间进行复制边界节点的信息传递以减少信息通信量,实现系统的全分布式DC-OPF计算。以6节点系统、IEEE-39节点系统分析全局变量的个数对迭代收敛的影响,并讨论风电并网对优化收敛的影响,最后通过仿真验证该文所提模型的准确性和有效性。
文摘通过增加伪码字的代价,基于交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)的惩罚译码方法可以改善低密度奇偶校验(Low-Density Parity-Check,LDPC)码低信噪比区域的译码性能,同时具有低的译码复杂度.而减少ADMM惩罚译码的欧几里德投影次数、选择合适的消息调度策略和设计有效的罚函数是提高ADMM惩罚译码速度的三种重要方法.为了进一步提高ADMM惩罚译码速度,通过利用Wei等人提出的方法来减少欧几里德投影的次数,本文设计了基于I-l1-PF罚函数的水平分层调度与垂直分层调度策略的两种LDPC码ADMM惩罚译码方法.仿真实验表明,与现有ADMM惩罚译码方法相比较,所设计的译码方法不仅具有较好的译码性能,而且能够显著降低LDPC码译码的平均迭代次数和平均译码时间.
文摘经典的非参数谱分析方法使用滑动窗口来捕捉大多数时间序列的频谱特性,然而这种方法不能很好地应用在时间序列的时频谱是时间连续的信号上.对于一些其时频谱满足时间连续频率稀疏的非平稳信号,提出了一种利用部分平行交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)求解谱寻求问题用于此类信号的时频分析方法.对一段加噪声的仿真信号和一段EEG(脑电)信号使用提出的方法进行时频分析.仿真结果表明:与短时傅里叶的分析方法相比,提出的方法不仅提高了时频谱的频率分辨率和时间分辨率,还有效抑制了噪声.最后从ADMM算法停止准则的角度说明了算法的收敛.
