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Distributed Subgradient Algorithm for Multi-Agent Optimization With Dynamic Stepsize 被引量:3
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作者 Xiaoxing Ren Dewei Li +1 位作者 Yugeng Xi Haibin Shao 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2021年第8期1451-1464,共14页
In this paper,we consider distributed convex optimization problems on multi-agent networks.We develop and analyze the distributed gradient method which allows each agent to compute its dynamic stepsize by utilizing th... In this paper,we consider distributed convex optimization problems on multi-agent networks.We develop and analyze the distributed gradient method which allows each agent to compute its dynamic stepsize by utilizing the time-varying estimate of the local function value at the global optimal solution.Our approach can be applied to both synchronous and asynchronous communication protocols.Specifically,we propose the distributed subgradient with uncoordinated dynamic stepsizes(DS-UD)algorithm for synchronous protocol and the AsynDGD algorithm for asynchronous protocol.Theoretical analysis shows that the proposed algorithms guarantee that all agents reach a consensus on the solution to the multi-agent optimization problem.Moreover,the proposed approach with dynamic stepsizes eliminates the requirement of diminishing stepsize in existing works.Numerical examples of distributed estimation in sensor networks are provided to illustrate the effectiveness of the proposed approach. 展开更多
关键词 Distributed optimization dynamic stepsize gradient method multi-agent networks
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Stepsize Selection in Explicit Runge-Kutta Methods for Moderately Stiff Problems
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作者 Justin Steven Calder Prentice 《Applied Mathematics》 2011年第6期711-717,共7页
We present an algorithm for determining the stepsize in an explicit Runge-Kutta method that is suitable when solving moderately stiff differential equations. The algorithm has a geometric character, and is based on a ... We present an algorithm for determining the stepsize in an explicit Runge-Kutta method that is suitable when solving moderately stiff differential equations. The algorithm has a geometric character, and is based on a pair of semicircles that enclose the boundary of the stability region in the left half of the complex plane. The algorithm includes an error control device. We describe a vectorized form of the algorithm, and present a corresponding MATLAB code. Numerical examples for Runge-Kutta methods of third and fourth order demonstrate the properties and capabilities of the algorithm. 展开更多
关键词 Moderately STIFF Problems RUNGE-KUTTA stepsize JACOBIAN Stability Region
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Self-Adaptive Stepsize Affine Projection Based Parameter Estimation of IPMSM Using Square-Wave Current Injection
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作者 Gaolin Wang Chen Li +1 位作者 Guoqiang Zhang Dianguo Xu 《CES Transactions on Electrical Machines and Systems》 2017年第1期48-57,共10页
Affine projection algorithm(APA)has been used to estimate the parameters of interior permanent magnet synchronous motor(IPMSM).However,there is not a strict guideline of choosing the stepsize of this algorithm to make... Affine projection algorithm(APA)has been used to estimate the parameters of interior permanent magnet synchronous motor(IPMSM).However,there is not a strict guideline of choosing the stepsize of this algorithm to make sure that the results of parameter estimation are convergent.In order to solve such problem,self-adaptive stepsize affine projection algorithm for parameter estimation of IPMSM is proposed in this paper.Compared with traditional affine projection algorithm,this method can obtain the stepsize automatically based on the operation condition,which can ensure the convergence and celerity of the process of parameter estimation.Then,on the basis of self-adaptive stepsize affine projection algorithm,a novel parameter estimation method based on square-wave current injection is proposed.By this method,the error of estimated parameter caused by stator resistance,linkage magnetic flux and dead-time voltage can be reduced effectively.Finally,the proposed parameter estimation method is verified by experiments on a 2.2-kW IPMSM drive platform. 展开更多
关键词 Affine projection parameter estimation permanent magnet synchronous machine square-current injection self-adaptive stepsize.
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Application of novel super-exponential iteration algorithm in underwater acoustic channel
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作者 NING Xiaoling FU Bing +3 位作者 ZHANG Linsen QIU Jiahao ZHU Lei FENG Chengxu 《Journal of Systems Engineering and Electronics》 SCIE CSCD 2024年第5期1122-1131,共10页
A novel variable step-size modified super-exponential iteration(MSEI)decision feedback blind equalization(DFE)algorithm with second-order digital phase-locked loop is put forward to improve the convergence performance... A novel variable step-size modified super-exponential iteration(MSEI)decision feedback blind equalization(DFE)algorithm with second-order digital phase-locked loop is put forward to improve the convergence performance of super-exponential iteration DFE algorithm.Based on the MSEI-DFE algorithm,it is first proposed to develop an error function as an improvement to the error function of MSEI,which effectively achieves faster convergence speed of the algorithm.Subsequently,a hyperbolic tangent function variable step-size algorithm is developed considering the high variation rate of the hyperbolic tangent function around zero,so as to further improve the convergence speed of the algorithm.In the end,a second-order digital phase-locked loop is introduced into the decision feedback equalizer to track and compensate for the phase rotation of equalizer input signals.For the multipath underwater acoustic channel with mixed phase and phase rotation,quadrature phase shift keying(QPSK)and 16 quadrature amplitude modulation(16QAM)modulated signals are used in the computer simulation of the algorithm in terms of convergence and carrier recovery performance.The results show that the proposed algorithm can considerably improve convergence speed and steady-state error,make effective compensation for phase rotation,and efficiently facilitate carrier recovery. 展开更多
关键词 super-exponential decision feedback variable stepsize phase rotation digital phase-locked loop underwater acoustic channel
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A NOTE ON THE GRADIENT PROJECTION METHOD WITH EXACT STEPSIZE RULE 被引量:2
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作者 Naihua Xiu Changyu Wang Lingchen Kong 《Journal of Computational Mathematics》 SCIE EI CSCD 2007年第2期221-230,共10页
In this paper, we give some convergence results on the gradient projection method with exact stepsize rule for solving the minimization problem with convex constraints. Especially, we show that if the objective functi... In this paper, we give some convergence results on the gradient projection method with exact stepsize rule for solving the minimization problem with convex constraints. Especially, we show that if the objective function is convex and its gradient is Lipschitz continuous, then the whole sequence of iterations produced by this method with bounded exact stepsizes converges to a solution of the concerned problem. 展开更多
关键词 Gradient projection method Exact stepsize rule Full convergence
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A Robust Decision Feedback Equalizer for ATSC DTV Receivers
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作者 秦雷 张文军 《Journal of Shanghai Jiaotong university(Science)》 EI 2008年第1期1-5,共5页
Least mean square (LMS) decision feedback equalizer (DFE) is preferred as an effective solution to coping with inter-symbol interference (ISI) for ATSC digital television (DTV) receivers. In DTV transmission environme... Least mean square (LMS) decision feedback equalizer (DFE) is preferred as an effective solution to coping with inter-symbol interference (ISI) for ATSC digital television (DTV) receivers. In DTV transmission environment, echo delay often covers several hundreds symbols, which leads to very large-scale equalizer. One consequence of the large-scale equalizer is the very slow convergence, which combined with error propagation, inherent drawback of DFE, seriously deteriorates the performance of the receivers, especially in severe channels More working modes and corresponding robust control mechanism were given to help the equalizer converge to the stable state smoothly. Simulation results show that the improved equalizer can perform better, especially in the severe channels. 展开更多
关键词 digital television (DTV) decision feedback equalizer robust control mechanism least mean square stepsize adjustment
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Linearized Proximal Alternating Direction Method of Multipliers for Parallel Magnetic Resonance Imaging
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作者 Benxin Zhang Zhibin Zhu 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2017年第4期763-769,共7页
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
关键词 Alternating direction method Barzilai-Borwein stepsize parallel magnetic resonance imaging total variation image reconstruction
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Modified Subgradient Extragradient Method for Pseudomonotone Variational Inequalities
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作者 Jiajia Cheng Hongwei Liu 《Journal of Harbin Institute of Technology(New Series)》 CAS 2022年第4期41-48,共8页
Many approaches have been put forward to resolve the variational inequality problem. The subgradient extragradient method is one of the most effective. This paper proposes a modified subgradient extragradient method a... Many approaches have been put forward to resolve the variational inequality problem. The subgradient extragradient method is one of the most effective. This paper proposes a modified subgradient extragradient method about classical variational inequality in a real Hilbert interspace. By analyzing the operator’s partial message, the proposed method designs a non-monotonic step length strategy which requires no line search and is independent of the value of Lipschitz constant, and is extended to solve the problem of pseudomonotone variational inequality. Meanwhile, the method requires merely one map value and a projective transformation to the practicable set at every iteration. In addition, without knowing the Lipschitz constant for interrelated mapping, weak convergence is given and R-linear convergence rate is established concerning algorithm. Several numerical results further illustrate that the method is superior to other algorithms. 展开更多
关键词 variational inequality subgradient extragradient method non⁃monotonic stepsize strategy pseudomonotone mapping
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Computational uncertainty principle in nonlinear ordinary differential equations (I)——Numerical results 被引量:20
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作者 李建平 曾庆存 丑纪范 《Science China(Technological Sciences)》 SCIE EI CAS 2000年第5期449-460,561,共13页
In a majority of cases of long-time numerical integration for initial-value problems, roundoff error has received little attention. Using twenty-nine numerical methods, the influence of round-off error on numerical so... In a majority of cases of long-time numerical integration for initial-value problems, roundoff error has received little attention. Using twenty-nine numerical methods, the influence of round-off error on numerical solutions is generally studied through a large number of numerical experiments. Here we find that there exists a strong dependence on machine precision (which is a new kind of dependence different from the sensitive dependence on initial conditions), maximally effective computation time (MECT) and optimal stepsize (OS) in solving nonlinear ordinary differential equations (ODEs) in finite machine precision. And an optimal searching method for evaluating MECT and OS under finite machine precision is presented. The relationships between MECT, OS, the order of numerical method and machine precision are found. Numerical results show that round-off error plays a significant role in the above phenomena. Moreover, we find two universal relations which are independent of the types of ODEs, initial values and numerical schemes. Based on the results of numerical experiments, we present a computational uncertainty principle, which is a great challenge to the reliability of long-time numerical integration for nonlinear ODEs. 展开更多
关键词 ordinary differential equations (ODEs) COMPUTATIONAL uncertainty principle round-off ERROR DISCRETIZATION ERROR strong dependence on machine precision MAXIMALLY effective computation time (MECT) optimal stepsize (OS) universal relation no
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Computational uncertainty principle in nonlinear ordinary differential equations——Ⅱ.Theoretical analysis 被引量:18
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作者 李建平 曾庆存 丑纪范 《Science China(Technological Sciences)》 SCIE EI CAS 2001年第1期55-74,共20页
The error propagation for general numerical method in ordinarydifferential equations ODEs is studied. Three kinds of convergence, theoretical, numerical and actual convergences, are presented. The various components o... The error propagation for general numerical method in ordinarydifferential equations ODEs is studied. Three kinds of convergence, theoretical, numerical and actual convergences, are presented. The various components of round-off error occurring in floating-point computation are fully detailed. By introducing a new kind of recurrent inequality, the classical error bounds for linear multistep methods are essentially improved, and joining probabilistic theory the “normal” growth of accumulated round-off error is derived. Moreover, a unified estimate for the total error of general method is given. On the basis of these results, we rationally interpret the various phenomena found in the numerical experiments in part I of this paper and derive two universal relations which are independent of types of ODEs, initial values and numerical schemes and are consistent with the numerical results. Furthermore, we give the explicitly mathematical expression of the computational uncertainty principle and expound the intrinsic relation between two uncertainties which result from the inaccuracies of numerical method and calculating machine. 展开更多
关键词 computational uncertainty principle round-off error discretization error universal relation ma-chine precision maximally effective computation time (MECT) optimal stepsize (OS) convergence.
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