This paper develops a variational model for image noise removal using total curvature(TC), which is a high-order regularizer. The TC has the advantage of preserving image feature. Unfortunately, it also has the charac...This paper develops a variational model for image noise removal using total curvature(TC), which is a high-order regularizer. The TC has the advantage of preserving image feature. Unfortunately, it also has the characteristics of nonlinear, non-convex and non-smooth. Consequently, the numerical computation with the curvature regularization is difficult. In order to conquer the computation problem, the proposed model is transformed into an alternating optimization problem by importing auxiliary variables. Furthermore, based on alternating direction method of multipliers, we design a fast numerical approximation iterative scheme for proposed model. Finally, numerous experiments are implemented to indicate the advantages of the proposed model in image edge preserving, image contrast and corners preserving. Meanwhile, the high computational efficiency of the designed model is verified by comparing with traditional models, including the total variation(TV) and total Laplace(TL) model.展开更多
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 deman...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.展开更多
A novel algorithm, i.e. the fast alternating direction method of multipliers （ADMM）, is applied to solve the classical total-variation （ TV ）-based model for image reconstruction. First, the TV-based model is refo...A novel algorithm, i.e. the fast alternating direction method of multipliers （ADMM）, is applied to solve the classical total-variation （ TV ）-based model for image reconstruction. First, the TV-based model is reformulated as a linear equality constrained problem where the objective function is separable. Then, by introducing the augmented Lagrangian function, the two variables are alternatively minimized by the Gauss-Seidel idea. Finally, the dual variable is updated. Because the approach makes full use of the special structure of the problem and decomposes the original problem into several low-dimensional sub-problems, the per iteration computational complexity of the approach is dominated by two fast Fourier transforms. Elementary experimental results indicate that the proposed approach is more stable and efficient compared with some state-of-the-art algorithms.展开更多
In this paper, we consider the convergence of the generalized alternating direction method of multipliers（GADMM） for solving linearly constrained nonconvex minimization model whose objective contains coupled functio...In this paper, we consider the convergence of the generalized alternating direction method of multipliers（GADMM） for solving linearly constrained nonconvex minimization model whose objective contains coupled functions. Under the assumption that the augmented Lagrangian function satisfies the Kurdyka-Lojasiewicz inequality, we prove that the sequence generated by the GADMM converges to a critical point of the augmented Lagrangian function when the penalty parameter in the augmented Lagrangian function is sufficiently large. Moreover, we also present some sufficient conditions guaranteeing the sublinear and linear rate of convergence of the algorithm.展开更多
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
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
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 method of multipliers(ADMM)is a widely used method for solving many convex minimization models arising in signal and image processing.In this paper,we propose an inertial ADMM for solving a t...The alternating direction method of multipliers(ADMM)is a widely used method for solving many convex minimization models arising in signal and image processing.In this paper,we propose an inertial ADMM for solving a two-block separable convex minimization problem with linear equality constraints.This algorithm is obtained by making use of the inertial Douglas-Rachford splitting algorithm to the corresponding dual of the primal problem.We study the convergence analysis of the proposed algorithm in infinite-dimensional Hilbert spaces.Furthermore,we apply the proposed algorithm on the robust principal component analysis problem and also compare it with other state-of-the-art algorithms.Numerical results demonstrate the advantage of the proposed algorithm.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
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
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
Sensitivity encoding(SENSE)is a parallel magnetic resonance imaging(MRI)reconstruction model by utilizing the sensitivity information of receiver coils to achieve image reconstruction.The existing SENSE-based reconstr...Sensitivity encoding(SENSE)is a parallel magnetic resonance imaging(MRI)reconstruction model by utilizing the sensitivity information of receiver coils to achieve image reconstruction.The existing SENSE-based reconstruction algorithms usually used nonadaptive sparsifying transforms,resulting in a limited reconstruction accuracy.Therefore,we proposed a new model for accurate parallel MRI reconstruction by combining the L0 norm regularization term based on the efficient sum of outer products dictionary learning(SOUPDIL)with the SENSE model,called SOUPDIL-SENSE.The SOUPDIL-SENSE model is mainly solved by utilizing the variable splitting and alternating direction method of multipliers techniques.The experimental results on four human datasets show that the proposed algorithm effectively promotes the image sparsity,eliminates the noise and artifacts of the reconstructed images,and improves the reconstruction accuracy.展开更多
Advanced adiabatic compressed air energy storage(AA-CAES),with its dual capability for electricity-heat cogeneration and energy storage,offers significant potential as an energy hub for integrated electricity and heat...Advanced adiabatic compressed air energy storage(AA-CAES),with its dual capability for electricity-heat cogeneration and energy storage,offers significant potential as an energy hub for integrated electricity and heat systems(IEHS).While synergies in the electricity-heat market are known to enhance economic efficiency,it is hard to achieve cooperative operation due to the inherent differences among participants of IEHS and the absence of an incentive-compatible mechanism.To address this challenge,this paper proposes a Nash bargaining-based cooperative operation strategy for IEHS with AA-CAES.First,a cooperative alliance framework based on the Nash bargaining is proposed to optimize energy trading.Second,to overcome computational complexity,the non-convex,nonlinear Nash bargaining problem is decomposed into a two-stage optimization approach.In the first stage,a joint planning model maximizes the total profit of the alliance,determining the optimal energy interaction for each participant.In the second stage,a subsequent model ensures fair profit distribution by optimizing pricing and benefit-sharing mechanisms.Subsequently,a distributed solution strategy based on the self-adaptive alternating direction method of multipliers is utilized to preserve operator privacy and improve computational efficiency.Finally,case studies demonstrate that within the electricity-heat co-supply mode,the daily profit of AA-CAES can improve by approximately 4137.45 CNY.Meanwhile,through the proposed cooperative strategy,participants in the IEHS can obtain greater profits,which validates the effectiveness of this strategy.展开更多
In this paper,we investigate the convergence of the generalized Bregman alternating direction method of multipliers(ADMM)for solving nonconvex separable problems with linear constraints.This algorithm relaxes the requ...In this paper,we investigate the convergence of the generalized Bregman alternating direction method of multipliers(ADMM)for solving nonconvex separable problems with linear constraints.This algorithm relaxes the requirement of global Lipschitz continuity of differentiable functions that is often seen in many researches,and it incorporates the acceleration technique of the proximal point algorithm(PPA).As a result,the scope of application of the algorithm is broadened and its performance is enhanced.Under the assumption that the augmented Lagrangian function satisfies the Kurdyka-Lojasiewicz inequality,we demonstrate that the iterative sequence generated by the algorithm converges to a critical point of its augmented Lagrangian function when the penalty parameter in the augmented Lagrangian function is sufficiently large.Finally,we analyze the convergence rate of the algorithm.展开更多
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 app...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.展开更多
In this paper,we propose an image denoising algorithm for compressed sensing based on alternating direction method of multipliers(ADMM).We prove that the objective func-tion of the iterates approaches the optimal valu...In this paper,we propose an image denoising algorithm for compressed sensing based on alternating direction method of multipliers(ADMM).We prove that the objective func-tion of the iterates approaches the optimal value.We also prove the O(1/N)convergence rate of our algorithm in the ergodic sense.At the same time,simulation results show that our algorithm is more efficient in image denoising compared with existing methods.展开更多
The utilization of gradient operators is prevalent in image processing,as they effectively detect edges and provide directional information.However,these operators only differentiate the horizontal and vertical direct...The utilization of gradient operators is prevalent in image processing,as they effectively detect edges and provide directional information.However,these operators only differentiate the horizontal and vertical directions,ignoring details and causing loss of information in other directions.This paper introduces the shear gradient operator to overcome this limitation by capturing details accurately in multiple directions.It investigates the properties of the shear gradient operator and proposes the shear total variation(STV)norm for image deblurring.By combining non-convex regularization to avoid excessive penalty and retain image details,a novel deblurring model integrating the STV norm and the L_(1)/L_(2) minimization is proposed.The alternating direction method of multipliers(ADMM)algorithm is employed to solve this computationally challenging model,demonstrating exceptional performance in non-blind image deblurring through experiments.展开更多
针对复杂电磁环境中因低信噪比、快拍采样数据不足、非高斯杂波干扰及多径传播效应等导致的波达方向(Direction of Arrival,DOA)估计性能退化问题,本文提出了一种基于降维高阶累积量与低秩矩阵重构的多源相干信号的DOA估计算法。首先通...针对复杂电磁环境中因低信噪比、快拍采样数据不足、非高斯杂波干扰及多径传播效应等导致的波达方向(Direction of Arrival,DOA)估计性能退化问题,本文提出了一种基于降维高阶累积量与低秩矩阵重构的多源相干信号的DOA估计算法。首先通过构建四阶累积量矩阵扩展阵列孔径,抑制高斯噪声,提升欠定条件下的信号自由度;随后采用高效的降维策略,显著降低计算复杂度;最后通过交替方向乘子法求解低秩约束下的Toeplitz协方差矩阵重构问题,实现了复杂环境下多源相干信号的高精度定位。实验结果表明,本算法在低信噪比及少快拍数下对多源相干信号依然有出色的估计性能,兼具高精度和强抗干扰特性,有良好的工程实用价值。展开更多
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 rat...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.展开更多
基金supported by the National Natural Science Foundation of China(No.61602269)the China Postdoctoral Science Foundation(No.2015M571993)+1 种基金the Shandong Provincial Natural Science Foundation of China(No.ZR2017MD004)the Qingdao Postdoctoral Application Research Funded Project
文摘This paper develops a variational model for image noise removal using total curvature(TC), which is a high-order regularizer. The TC has the advantage of preserving image feature. Unfortunately, it also has the characteristics of nonlinear, non-convex and non-smooth. Consequently, the numerical computation with the curvature regularization is difficult. In order to conquer the computation problem, the proposed model is transformed into an alternating optimization problem by importing auxiliary variables. Furthermore, based on alternating direction method of multipliers, we design a fast numerical approximation iterative scheme for proposed model. Finally, numerous experiments are implemented to indicate the advantages of the proposed model in image edge preserving, image contrast and corners preserving. Meanwhile, the high computational efficiency of the designed model is verified by comparing with traditional models, including the total variation(TV) and total Laplace(TL) model.
基金This work was supported by the National Key R&D Program of China(No.2018YFB0905000)the Science and Technology Project of State Grid Corporation of China(No.SGTJDK00DWJS1800232).
文摘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.
基金The Scientific Research Foundation of Nanjing University of Posts and Telecommunications(No.NY210049)
文摘A novel algorithm, i.e. the fast alternating direction method of multipliers （ADMM）, is applied to solve the classical total-variation （ TV ）-based model for image reconstruction. First, the TV-based model is reformulated as a linear equality constrained problem where the objective function is separable. Then, by introducing the augmented Lagrangian function, the two variables are alternatively minimized by the Gauss-Seidel idea. Finally, the dual variable is updated. Because the approach makes full use of the special structure of the problem and decomposes the original problem into several low-dimensional sub-problems, the per iteration computational complexity of the approach is dominated by two fast Fourier transforms. Elementary experimental results indicate that the proposed approach is more stable and efficient compared with some state-of-the-art algorithms.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1157117811801455)the Fundamental Research Funds of China West Normal University(Grant No.17E084)
文摘In this paper, we consider the convergence of the generalized alternating direction method of multipliers（GADMM） for solving linearly constrained nonconvex minimization model whose objective contains coupled functions. Under the assumption that the augmented Lagrangian function satisfies the Kurdyka-Lojasiewicz inequality, we prove that the sequence generated by the GADMM converges to a critical point of the augmented Lagrangian function when the penalty parameter in the augmented Lagrangian function is sufficiently large. Moreover, we also present some sufficient conditions guaranteeing the sublinear and linear rate of convergence of the algorithm.
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.
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.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12061045,12061046,11661056,11771198,11771347,91730306,41390454,11401293)the China Postdoctoral Science Foundation(Grant No.2015M571989)the Jiangxi Province Postdoctoral Science Foundation(Grant No.2015KY51)。
文摘The alternating direction method of multipliers(ADMM)is a widely used method for solving many convex minimization models arising in signal and image processing.In this paper,we propose an inertial ADMM for solving a two-block separable convex minimization problem with linear equality constraints.This algorithm is obtained by making use of the inertial Douglas-Rachford splitting algorithm to the corresponding dual of the primal problem.We study the convergence analysis of the proposed algorithm in infinite-dimensional Hilbert spaces.Furthermore,we apply the proposed algorithm on the robust principal component analysis problem and also compare it with other state-of-the-art algorithms.Numerical results demonstrate the advantage of the proposed algorithm.
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the National Natural Science Foundation of China(No.61861023)the Yunnan Fundamental Research Project(No.202301AT070452)。
文摘Sensitivity encoding(SENSE)is a parallel magnetic resonance imaging(MRI)reconstruction model by utilizing the sensitivity information of receiver coils to achieve image reconstruction.The existing SENSE-based reconstruction algorithms usually used nonadaptive sparsifying transforms,resulting in a limited reconstruction accuracy.Therefore,we proposed a new model for accurate parallel MRI reconstruction by combining the L0 norm regularization term based on the efficient sum of outer products dictionary learning(SOUPDIL)with the SENSE model,called SOUPDIL-SENSE.The SOUPDIL-SENSE model is mainly solved by utilizing the variable splitting and alternating direction method of multipliers techniques.The experimental results on four human datasets show that the proposed algorithm effectively promotes the image sparsity,eliminates the noise and artifacts of the reconstructed images,and improves the reconstruction accuracy.
基金supported in part by the National Natural Science Foundation of China(No.52407115)State Key Laboratory of Power System Operation and Control(61011000223).
文摘Advanced adiabatic compressed air energy storage(AA-CAES),with its dual capability for electricity-heat cogeneration and energy storage,offers significant potential as an energy hub for integrated electricity and heat systems(IEHS).While synergies in the electricity-heat market are known to enhance economic efficiency,it is hard to achieve cooperative operation due to the inherent differences among participants of IEHS and the absence of an incentive-compatible mechanism.To address this challenge,this paper proposes a Nash bargaining-based cooperative operation strategy for IEHS with AA-CAES.First,a cooperative alliance framework based on the Nash bargaining is proposed to optimize energy trading.Second,to overcome computational complexity,the non-convex,nonlinear Nash bargaining problem is decomposed into a two-stage optimization approach.In the first stage,a joint planning model maximizes the total profit of the alliance,determining the optimal energy interaction for each participant.In the second stage,a subsequent model ensures fair profit distribution by optimizing pricing and benefit-sharing mechanisms.Subsequently,a distributed solution strategy based on the self-adaptive alternating direction method of multipliers is utilized to preserve operator privacy and improve computational efficiency.Finally,case studies demonstrate that within the electricity-heat co-supply mode,the daily profit of AA-CAES can improve by approximately 4137.45 CNY.Meanwhile,through the proposed cooperative strategy,participants in the IEHS can obtain greater profits,which validates the effectiveness of this strategy.
文摘In this paper,we investigate the convergence of the generalized Bregman alternating direction method of multipliers(ADMM)for solving nonconvex separable problems with linear constraints.This algorithm relaxes the requirement of global Lipschitz continuity of differentiable functions that is often seen in many researches,and it incorporates the acceleration technique of the proximal point algorithm(PPA).As a result,the scope of application of the algorithm is broadened and its performance is enhanced.Under the assumption that the augmented Lagrangian function satisfies the Kurdyka-Lojasiewicz inequality,we demonstrate that the iterative sequence generated by the algorithm converges to a critical point of its augmented Lagrangian function when the penalty parameter in the augmented Lagrangian function is sufficiently large.Finally,we analyze the convergence rate of the algorithm.
基金supported by National Natural Science Foundation of China(Grant Nos.11001124 and 91130007)the Doctoral Fund of Ministry of Eduction of China(Grant No.20110091110004)the General Research Fund from Hong Kong Research Grants Council(Grant No.HKBU 203712)
文摘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.
基金This work is partially supported by the National Natural Science Foundation of China(No.11771350)Basic and Advanced Research Project of CQ CSTC(Nos.cstc2020jcyj-msxmX0738 and cstc2018jcyjAX0605).
文摘In this paper,we propose an image denoising algorithm for compressed sensing based on alternating direction method of multipliers(ADMM).We prove that the objective func-tion of the iterates approaches the optimal value.We also prove the O(1/N)convergence rate of our algorithm in the ergodic sense.At the same time,simulation results show that our algorithm is more efficient in image denoising compared with existing methods.
基金Supported by the National Natural Science Foundation of China(61701004)。
文摘The utilization of gradient operators is prevalent in image processing,as they effectively detect edges and provide directional information.However,these operators only differentiate the horizontal and vertical directions,ignoring details and causing loss of information in other directions.This paper introduces the shear gradient operator to overcome this limitation by capturing details accurately in multiple directions.It investigates the properties of the shear gradient operator and proposes the shear total variation(STV)norm for image deblurring.By combining non-convex regularization to avoid excessive penalty and retain image details,a novel deblurring model integrating the STV norm and the L_(1)/L_(2) minimization is proposed.The alternating direction method of multipliers(ADMM)algorithm is employed to solve this computationally challenging model,demonstrating exceptional performance in non-blind image deblurring through experiments.
文摘针对复杂电磁环境中因低信噪比、快拍采样数据不足、非高斯杂波干扰及多径传播效应等导致的波达方向(Direction of Arrival,DOA)估计性能退化问题,本文提出了一种基于降维高阶累积量与低秩矩阵重构的多源相干信号的DOA估计算法。首先通过构建四阶累积量矩阵扩展阵列孔径,抑制高斯噪声,提升欠定条件下的信号自由度;随后采用高效的降维策略,显著降低计算复杂度;最后通过交替方向乘子法求解低秩约束下的Toeplitz协方差矩阵重构问题,实现了复杂环境下多源相干信号的高精度定位。实验结果表明,本算法在低信噪比及少快拍数下对多源相干信号依然有出色的估计性能,兼具高精度和强抗干扰特性,有良好的工程实用价值。
基金This work is supported by the National Natural Science Foundation of China(Nos.11625105 and 12131004).
文摘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.
