Linear scan computed tomography (LCT) is of great benefit to online industrial scanning and security inspection due to its characteristics of straight-line source trajectory and high scanning speed. However, in prac...Linear scan computed tomography (LCT) is of great benefit to online industrial scanning and security inspection due to its characteristics of straight-line source trajectory and high scanning speed. However, in practical applications of LCT, there are challenges to image reconstruction due to limited-angle and insufficient data. In this paper, a new reconstruction algorithm based on total-variation (TV) minimization is developed to reconstruct images from limited-angle and insufficient data in LCT. The main idea of our approach is to reformulate a TV problem as a linear equality constrained problem where the objective function is separable, and then minimize its augmented Lagrangian function by using alternating direction method (ADM) to solve subproblems. The proposed method is robust and efficient in the task of reconstruction by showing the convergence of ADM. The numerical simulations and real data reconstructions show that the proposed reconstruction method brings reasonable performance and outperforms some previous ones when applied to an LCT imaging problem.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
This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite differenc...This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite difference scheme with second-order splitting error, the other two schemes have third-order splitting error, and the last one is an extended LOD scheme. The L2 norm and H1 semi-norm error estimates are obtained for the first scheme and second one, respectively. Finally, two numerical examples are provided to illustrate the efficiency and accuracy of the methods.展开更多
In this study, we propose a linearized proximal alternating direction method with variable stepsize for solving total variation image reconstruction problems. Our method uses a linearized technique and the proximal fu...In this study, we propose a linearized proximal alternating direction method with variable stepsize for solving total variation image reconstruction problems. Our method uses a linearized technique and the proximal function such that the closed form solutions of the subproblem can be easily derived.In the subproblem, we apply a variable stepsize, that is like Barzilai-Borwein stepsize, to accelerate the algorithm. Numerical results with parallel magnetic resonance imaging demonstrate the efficiency of the proposed algorithm.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
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
In the contemporary era, the proliferation of information technology has led to an unprecedented surge in data generation, with this data being dispersed across a multitude of mobile devices. Facing these situations a...In the contemporary era, the proliferation of information technology has led to an unprecedented surge in data generation, with this data being dispersed across a multitude of mobile devices. Facing these situations and the training of deep learning model that needs great computing power support, the distributed algorithm that can carry out multi-party joint modeling has attracted everyone’s attention. The distributed training mode relieves the huge pressure of centralized model on computer computing power and communication. However, most distributed algorithms currently work in a master-slave mode, often including a central server for coordination, which to some extent will cause communication pressure, data leakage, privacy violations and other issues. To solve these problems, a decentralized fully distributed algorithm based on deep random weight neural network is proposed. The algorithm decomposes the original objective function into several sub-problems under consistency constraints, combines the decentralized average consensus (DAC) and alternating direction method of multipliers (ADMM), and achieves the goal of joint modeling and training through local calculation and communication of each node. Finally, we compare the proposed decentralized algorithm with several centralized deep neural networks with random weights, and experimental results demonstrate the effectiveness of the proposed algorithm.展开更多
To improve the accuracy and effectiveness of continuous-time(CT) system identification, this paper introduces a novel method that incorporates the nuclear norm minimization(NNM) with the generalized Poisson moment fun...To improve the accuracy and effectiveness of continuous-time(CT) system identification, this paper introduces a novel method that incorporates the nuclear norm minimization(NNM) with the generalized Poisson moment functional(GPMF)based subspace method. The GPMF algorithm provides a simple linear mapping for subspace identification without the timederivatives of the input and output measurements to avoid amplification of measurement noise, and the NNM is a heuristic convex relaxation of the rank minimization. The Hankel matrix with minimized nuclear norm is used to determine the model order and to avoid the over-parameterization in subspace identification method(SIM). Furthermore, the algorithm to solve the NNM problem in CT case is also deduced with alternating direction methods of multipliers(ADMM). Lastly, two numerical examples are presented to evaluate the performance of the proposed method and to show the advantages of the proposed method over the existing methods.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
In this paper,two classes of Riesz space fractional partial differential equations including space-fractional and space-time-fractional ones are considered.These two models can be regarded as the generalization of the...In this paper,two classes of Riesz space fractional partial differential equations including space-fractional and space-time-fractional ones are considered.These two models can be regarded as the generalization of the classical wave equation in two space dimensions.Combining with the Crank-Nicolson method in temporal direction,efficient alternating direction implicit Galerkin finite element methods for solving these two fractional models are developed,respectively.The corresponding stability and convergence analysis of the numerical methods are discussed.Numerical results are provided to verify the theoretical analysis.展开更多
The imaging speed is a bottleneck for magnetic resonance imaging( MRI) since it appears. To alleviate this difficulty,a novel graph regularized sparse coding method for highly undersampled MRI reconstruction( GSCMRI) ...The imaging speed is a bottleneck for magnetic resonance imaging( MRI) since it appears. To alleviate this difficulty,a novel graph regularized sparse coding method for highly undersampled MRI reconstruction( GSCMRI) was proposed. The graph regularized sparse coding showed the potential in maintaining the geometrical information of the data. In this study, it was incorporated with two-level Bregman iterative procedure that updated the data term in outer-level and learned dictionary in innerlevel. Moreover,the graph regularized sparse coding and simple dictionary updating stages derived by the inner minimization made the proposed algorithm converge in few iterations, meanwhile achieving superior reconstruction performance. Extensive experimental results have demonstrated GSCMRI can consistently recover both real-valued MR images and complex-valued MR data efficiently,and outperform the current state-of-the-art approaches in terms of higher PSNR and lower HFEN values.展开更多
Numerical simulation of complex flow fields with multi-scale structures is one of the most important and challenging branches of computational fluid dynamics. From linear analysis and numerical experiments it has been...Numerical simulation of complex flow fields with multi-scale structures is one of the most important and challenging branches of computational fluid dynamics. From linear analysis and numerical experiments it has been discovered that the higher-order accurate method can give reliable and efficient computational results, as well as better resolution of the complex flow fields with multi-scale structures. Compact finite difference schemes, which feature higher-order accuracy and spectral-like resolution with smaller stencils and easier application of boundary conditions, has attracted more and more interest and attention.展开更多
An alternating direction implicit (ADI) Galerkin method with moving finite element spaces is formulated for a class of second order hyperbolic equations in two space variables. A priori H 1 error estimate is derived.
Based on rectangular partition and bilinear interpolation,we construct an alternating-direction implicit(ADI)finite volume element method,which combined the merits of finite volume element method and alternating direc...Based on rectangular partition and bilinear interpolation,we construct an alternating-direction implicit(ADI)finite volume element method,which combined the merits of finite volume element method and alternating direction implicit method to solve a viscous wave equation with variable coefficients.This paper presents a general procedure to construct the alternating-direction implicit finite volume element method and gives computational schemes.Optimal error estimate in L2 norm is obtained for the schemes.Compared with the finite volume element method of the same convergence order,our method is more effective in terms of running time with the increasing of the computing scale.Numerical experiments are presented to show the efficiency of our method and numerical results are provided to support our theoretical analysis.展开更多
The sparse phase retrieval aims to recover the sparse signal from quadratic measurements. However, the measurements are often affected by outliers and asymmetric distribution noise. This paper introduces a novel metho...The sparse phase retrieval aims to recover the sparse signal from quadratic measurements. However, the measurements are often affected by outliers and asymmetric distribution noise. This paper introduces a novel method that combines the quantile regression and the L<sub>1/2</sub>-regularizer. It is a non-convex, non-smooth, non-Lipschitz optimization problem. We propose an efficient algorithm based on the Alternating Direction Methods of Multiplier (ADMM) to solve the corresponding optimization problem. Numerous numerical experiments show that this method can recover sparse signals with fewer measurements and is robust to dense bounded noise and Laplace noise.展开更多
In this paper, an alternating direction nonmonotone approximate Newton algorithm (ADNAN) based on nonmonotone line search is developed for solving inverse problems. It is shown that ADNAN converges to a solution of th...In this paper, an alternating direction nonmonotone approximate Newton algorithm (ADNAN) based on nonmonotone line search is developed for solving inverse problems. It is shown that ADNAN converges to a solution of the inverse problems and numerical results provide the effectiveness of the proposed algorithm.展开更多
In this paper, an alternating direction Galerkin finite element method is presented for solving 2D time fractional reaction sub-diffusion equation with nonlinear source term. Firstly, one order implicit-explicit metho...In this paper, an alternating direction Galerkin finite element method is presented for solving 2D time fractional reaction sub-diffusion equation with nonlinear source term. Firstly, one order implicit-explicit method is used for time discretization, then Galerkin finite element method is adopted for spatial discretization and obtain a fully discrete linear system. Secondly, Galerkin alternating direction procedure for the system is derived by adding an extra term. Finally, the stability and convergence of the method are analyzed rigorously. Numerical results confirm the accuracy and efficiency of the proposed method.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 order to rapidly and accurately detect infrared small and dim targets in the infrared image of complex scene collected by virtual prototyping of space-based downward-looking multiband detection,an improved detectio...In order to rapidly and accurately detect infrared small and dim targets in the infrared image of complex scene collected by virtual prototyping of space-based downward-looking multiband detection,an improved detection algorithm of infrared small and dim target is proposed in this paper.Firstly,the original infrared images are changed into a new infrared patch tensor mode through data reconstruction.Then,the infrared small and dim target detection problems are converted to low-rank tensor recovery problems based on tensor nuclear norm in accordance with patch tensor characteristics,and inverse variance weighted entropy is defined for self-adaptive adjustment of sparseness.Finally,the low-rank tensor recovery problem with noise is solved by alternating the direction method to obtain the sparse target image,and the final small target is worked out by a simple partitioning algorithm.The test results in various spacebased downward-looking complex scenes show that such method can restrain complex background well by virtue of rapid arithmetic speed with high detection probability and low false alarm rate.It is a kind of infrared small and dim target detection method with good performance.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
基金the National High Technology Research and Development Program of China(Grant No.2012AA011603)
文摘Linear scan computed tomography (LCT) is of great benefit to online industrial scanning and security inspection due to its characteristics of straight-line source trajectory and high scanning speed. However, in practical applications of LCT, there are challenges to image reconstruction due to limited-angle and insufficient data. In this paper, a new reconstruction algorithm based on total-variation (TV) minimization is developed to reconstruct images from limited-angle and insufficient data in LCT. The main idea of our approach is to reformulate a TV problem as a linear equality constrained problem where the objective function is separable, and then minimize its augmented Lagrangian function by using alternating direction method (ADM) to solve subproblems. The proposed method is robust and efficient in the task of reconstruction by showing the convergence of ADM. The numerical simulations and real data reconstructions show that the proposed reconstruction method brings reasonable performance and outperforms some previous ones when applied to an LCT imaging problem.
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.
文摘This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite difference scheme with second-order splitting error, the other two schemes have third-order splitting error, and the last one is an extended LOD scheme. The L2 norm and H1 semi-norm error estimates are obtained for the first scheme and second one, respectively. Finally, two numerical examples are provided to illustrate the efficiency and accuracy of the methods.
基金supported in part by the National Natural Science Foundation of China(11361018,11461015)Guangxi Natural Science Foundation(2014GXNSFFA118001)+3 种基金Guangxi Key Laboratory of Automatic Detecting Technology and Instruments(YQ15112,YQ16112)Guilin Science and Technology Project(20140127-2)the Innovation Project of Guangxi Graduate Education and Innovation Project of GUET Graduate Education(YJCXB201502)Guangxi Key Laboratory of Cryptography and Information Security(GCIS201624)
文摘In this study, we propose a linearized proximal alternating direction method with variable stepsize for solving total variation image reconstruction problems. Our method uses a linearized technique and the proximal function such that the closed form solutions of the subproblem can be easily derived.In the subproblem, we apply a variable stepsize, that is like Barzilai-Borwein stepsize, to accelerate the algorithm. Numerical results with parallel magnetic resonance imaging demonstrate the efficiency of the proposed algorithm.
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In the contemporary era, the proliferation of information technology has led to an unprecedented surge in data generation, with this data being dispersed across a multitude of mobile devices. Facing these situations and the training of deep learning model that needs great computing power support, the distributed algorithm that can carry out multi-party joint modeling has attracted everyone’s attention. The distributed training mode relieves the huge pressure of centralized model on computer computing power and communication. However, most distributed algorithms currently work in a master-slave mode, often including a central server for coordination, which to some extent will cause communication pressure, data leakage, privacy violations and other issues. To solve these problems, a decentralized fully distributed algorithm based on deep random weight neural network is proposed. The algorithm decomposes the original objective function into several sub-problems under consistency constraints, combines the decentralized average consensus (DAC) and alternating direction method of multipliers (ADMM), and achieves the goal of joint modeling and training through local calculation and communication of each node. Finally, we compare the proposed decentralized algorithm with several centralized deep neural networks with random weights, and experimental results demonstrate the effectiveness of the proposed algorithm.
文摘To improve the accuracy and effectiveness of continuous-time(CT) system identification, this paper introduces a novel method that incorporates the nuclear norm minimization(NNM) with the generalized Poisson moment functional(GPMF)based subspace method. The GPMF algorithm provides a simple linear mapping for subspace identification without the timederivatives of the input and output measurements to avoid amplification of measurement noise, and the NNM is a heuristic convex relaxation of the rank minimization. The Hankel matrix with minimized nuclear norm is used to determine the model order and to avoid the over-parameterization in subspace identification method(SIM). Furthermore, the algorithm to solve the NNM problem in CT case is also deduced with alternating direction methods of multipliers(ADMM). Lastly, two numerical examples are presented to evaluate the performance of the proposed method and to show the advantages of the proposed method over the existing methods.
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 by the Guangxi Natural Science Foundation[grant numbers 2018GXNSFBA281020,2018GXNSFAA138121]the Doctoral Starting up Foundation of Guilin University of Technology[grant number GLUTQD2016044].
文摘In this paper,two classes of Riesz space fractional partial differential equations including space-fractional and space-time-fractional ones are considered.These two models can be regarded as the generalization of the classical wave equation in two space dimensions.Combining with the Crank-Nicolson method in temporal direction,efficient alternating direction implicit Galerkin finite element methods for solving these two fractional models are developed,respectively.The corresponding stability and convergence analysis of the numerical methods are discussed.Numerical results are provided to verify the theoretical analysis.
基金National Natural Science Foundations of China(Nos.61362001,61102043,61262084)Technology Foundations of Department of Education of Jiangxi Province,China(Nos.GJJ12006,GJJ14196)Natural Science Foundations of Jiangxi Province,China(Nos.20132BAB211030,20122BAB211015)
文摘The imaging speed is a bottleneck for magnetic resonance imaging( MRI) since it appears. To alleviate this difficulty,a novel graph regularized sparse coding method for highly undersampled MRI reconstruction( GSCMRI) was proposed. The graph regularized sparse coding showed the potential in maintaining the geometrical information of the data. In this study, it was incorporated with two-level Bregman iterative procedure that updated the data term in outer-level and learned dictionary in innerlevel. Moreover,the graph regularized sparse coding and simple dictionary updating stages derived by the inner minimization made the proposed algorithm converge in few iterations, meanwhile achieving superior reconstruction performance. Extensive experimental results have demonstrated GSCMRI can consistently recover both real-valued MR images and complex-valued MR data efficiently,and outperform the current state-of-the-art approaches in terms of higher PSNR and lower HFEN values.
文摘Numerical simulation of complex flow fields with multi-scale structures is one of the most important and challenging branches of computational fluid dynamics. From linear analysis and numerical experiments it has been discovered that the higher-order accurate method can give reliable and efficient computational results, as well as better resolution of the complex flow fields with multi-scale structures. Compact finite difference schemes, which feature higher-order accuracy and spectral-like resolution with smaller stencils and easier application of boundary conditions, has attracted more and more interest and attention.
基金the National Natural Sciences Foundation of China
文摘An alternating direction implicit (ADI) Galerkin method with moving finite element spaces is formulated for a class of second order hyperbolic equations in two space variables. A priori H 1 error estimate is derived.
基金supported by the National Natural Science Foundation of China grants No.11971241.
文摘Based on rectangular partition and bilinear interpolation,we construct an alternating-direction implicit(ADI)finite volume element method,which combined the merits of finite volume element method and alternating direction implicit method to solve a viscous wave equation with variable coefficients.This paper presents a general procedure to construct the alternating-direction implicit finite volume element method and gives computational schemes.Optimal error estimate in L2 norm is obtained for the schemes.Compared with the finite volume element method of the same convergence order,our method is more effective in terms of running time with the increasing of the computing scale.Numerical experiments are presented to show the efficiency of our method and numerical results are provided to support our theoretical analysis.
文摘The sparse phase retrieval aims to recover the sparse signal from quadratic measurements. However, the measurements are often affected by outliers and asymmetric distribution noise. This paper introduces a novel method that combines the quantile regression and the L<sub>1/2</sub>-regularizer. It is a non-convex, non-smooth, non-Lipschitz optimization problem. We propose an efficient algorithm based on the Alternating Direction Methods of Multiplier (ADMM) to solve the corresponding optimization problem. Numerous numerical experiments show that this method can recover sparse signals with fewer measurements and is robust to dense bounded noise and Laplace noise.
文摘In this paper, an alternating direction nonmonotone approximate Newton algorithm (ADNAN) based on nonmonotone line search is developed for solving inverse problems. It is shown that ADNAN converges to a solution of the inverse problems and numerical results provide the effectiveness of the proposed algorithm.
文摘In this paper, an alternating direction Galerkin finite element method is presented for solving 2D time fractional reaction sub-diffusion equation with nonlinear source term. Firstly, one order implicit-explicit method is used for time discretization, then Galerkin finite element method is adopted for spatial discretization and obtain a fully discrete linear system. Secondly, Galerkin alternating direction procedure for the system is derived by adding an extra term. Finally, the stability and convergence of the method are analyzed rigorously. Numerical results confirm the accuracy and efficiency of the proposed method.
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 order to rapidly and accurately detect infrared small and dim targets in the infrared image of complex scene collected by virtual prototyping of space-based downward-looking multiband detection,an improved detection algorithm of infrared small and dim target is proposed in this paper.Firstly,the original infrared images are changed into a new infrared patch tensor mode through data reconstruction.Then,the infrared small and dim target detection problems are converted to low-rank tensor recovery problems based on tensor nuclear norm in accordance with patch tensor characteristics,and inverse variance weighted entropy is defined for self-adaptive adjustment of sparseness.Finally,the low-rank tensor recovery problem with noise is solved by alternating the direction method to obtain the sparse target image,and the final small target is worked out by a simple partitioning algorithm.The test results in various spacebased downward-looking complex scenes show that such method can restrain complex background well by virtue of rapid arithmetic speed with high detection probability and low false alarm rate.It is a kind of infrared small and dim target detection method with good performance.
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.