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ON ITERATIVE ALGORITHMS FOR A CLASS OF NONLINEAR VARIATIONAL INEQUALITIES 认领 引用
1
作者 M. A. Moor 《Analysis in Theory and Applications》 1995年第3期95-105,共11页
In this paper we use the auxiliary principle technique to suggest and analyze novel and innovative iterative algorithms for a class of nonlinear variational inequalities. Several special cases, which can be obtained f... In this paper we use the auxiliary principle technique to suggest and analyze novel and innovative iterative algorithms for a class of nonlinear variational inequalities. Several special cases, which can be obtained from our main results, are also discussed. 展开更多
关键词 ON ITERATIVE ALGORITHMS FOR A CLASS OF NONLINEAR VARIATIONAL INEQUALITIES
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Improved gradient iterative algorithms for solving Lyapunov matrix equations 认领 引用 被引量：1
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作者 顾传青 范伟薇 《Journal of Shanghai University(English Edition)》 2008年第5期395-399,共5页
In this paper, an improved gradient iterative （GI） algorithm for solving the Lyapunov matrix equations is studied. Convergence of the improved method for any initial value is proved with some conditions. Compared wi... In this paper, an improved gradient iterative （GI） algorithm for solving the Lyapunov matrix equations is studied. Convergence of the improved method for any initial value is proved with some conditions. Compared with the GI algorithm, the improved algorithm reduces computational cost and storage. Finally, the algorithm is tested with GI several numerical examples. 展开更多
关键词 gradient iterative （GI） algorithm improved gradient iteration （GI） algorithm Lyapunov matrix equations convergence factor
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Auxiliary principle and three-step iterative algorithms for generalized set-valued strongly nonlinear mixed variational-like inequalities 认领 引用 被引量：1
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作者 徐海丽 郭兴明 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第6期721-729,共9页
An auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities is extended. The existence and uniqueness of the solution of the auxiliary problem for... An auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities is extended. The existence and uniqueness of the solution of the auxiliary problem for the generalized set-valued strongly nonlinear mixed variational-like inequalities are proved, a novel and innovative three-step iterative algorithm to compute approximate solution is constructed, and the existence of the solution of the generalized set-valued strongly nonlinear mixed variational-like inequality is shown using the auxiliary principle iterative sequences generated by the algorithm technique. The convergence of three-step is also proved. 展开更多
关键词 mixed variational-like inequality three-step iterative algorithm set-valued mapping auxiliary principle technique
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SOME NEW ITERATIVE ALGORITHMS FOR MONOTONE MIXED VARIATIONAL INEQUALITIES 认领 引用 被引量：4
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作者 Zhang XianDept. of Basic Courses,Jimei Univ.,Xiamen 361021. 《Applied Mathematics(A Journal of Chinese Universities)》 2002年第1期80-84,共5页
In this paper,some new iterative algorithms for monotone mixed variational inequalities and the convergence in real Hilbert spaces are studied.
关键词 mixed variational inequality iterative algorithm monotone operator. Supported by Natural Science Foundation of Education Council of Fujian Province of China.
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Radar Imaging Based on Iterative Algorithms 认领 引用
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作者 Qiangfu Zhao, Zhong Wang and Youan KeDept. of Electronic Eng., Beijing Institute of Technology, P.O.Box 327, Beijing 100081, China 《Journal of Systems Engineering and Electronics》 1991年第2期91-99,共9页
It has long been realized that the problem of radar imaging is a special case of image reconstruction in which the data are incomplete and noisy. In other fields, iterative reconstruction algorithms have been used suc... It has long been realized that the problem of radar imaging is a special case of image reconstruction in which the data are incomplete and noisy. In other fields, iterative reconstruction algorithms have been used successfully to improve the image quality. This paper studies the application of iterative algorithms in radar imaging. A discrete model is first derived, and the iterative algorithms are then adapted to radar imaging. Although such algorithms are usually time consuming, this paper shows that, if the algorithms are appropriately simplified, it is possible to realize them even in real time. The efficiency of iterative algorithms is shown through computer simulations. 展开更多
关键词 Radar imaging Computerized tomography Discrete model Iterative reconstruction algorithm Algebraic reconstruction technique.
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Distributed Iterative Learning Control for Load Balancing in Flexible AC/DC Hybrid Distribution Systems 认领 引用
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作者 Hong Zhang Bin Xu +4 位作者 Jinzhong Li Xiaoxiao Meng Cheng Qian Wei Ma Yuguang Xie 《Energy Engineering》 EI 2026年第5期298-316,共19页
The increasing integration of distributed renewable energy sources in the distribution network leads to unbalanced load rates in the distribution network.The traditional load balancing methods are mainly based on netw... The increasing integration of distributed renewable energy sources in the distribution network leads to unbalanced load rates in the distribution network.The traditional load balancing methods are mainly based on network reconfiguration,which have problems such as a long time scale and poor adaptability.In response to these issues,this paper proposes a distributed iterative learning control(ILC)strategy for load balancing in flexible AC/DC hybrid distribution systems.This method combines the consensus algorithm with the ILC mechanism to construct a multi-terminal AC/DC flexible interconnection system model.It is only necessary to measure the load rate of adjacent units without observing the overall system status,which greatly reduces complexity and enhances robustness.In this paper,a new energy photovoltaic and energy storage integrated system was built through MATLAB/Simulink simulation,and the effectiveness of the proposed strategy under normal working conditions and port faults was verified through this system.Through comparative studies with event-triggered control and traditional consensus algorithms,as well as real-time simulations on the RT-LAB simulation platform,it has been confirmed that this method has superior performance in terms of convergence speed,steady-state accuracy,and dynamic response,and has the potential to be applied in practical models.It is suitable for application in medium and low voltage distribution systems with new energy access. 展开更多
关键词 AC/DC hybrid distribution systems iterative learning algorithm load rate
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TWO PARALLEL ALGORITHMS FOR A CLASS OF SPLIT COMMON SOLUTION PROBLEMS 认领 引用
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作者 Truong Minh TUYEN Nguyen Thi TRANG Tran Thi HUONG 《Acta Mathematica Scientia》 SCIE CSCD 2026年第1期505-518,共14页
We study the split common solution problem with multiple output sets for monotone operator equations in Hilbert spaces.To solve this problem,we propose two new parallel algorithms.We establish a weak convergence theor... We study the split common solution problem with multiple output sets for monotone operator equations in Hilbert spaces.To solve this problem,we propose two new parallel algorithms.We establish a weak convergence theorem for the first and a strong convergence theorem for the second. 展开更多
关键词 iterative algorithm Hilbert space metric projection proximal point algorithm
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Iterative algorithms with the latest update for Riccati matrix equations in Ito Markov jump systems 认领 引用 被引量：1
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作者 MA Chuang LI Zhi +1 位作者 WU WanQi ZHANG Ying 《Science China(Technological Sciences)》 SCIE EI CAS CSCD 2020年第8期1577-1584,共8页
This study is concerned with the problem to solve the continuous coupled Riccati matrix equations in It?Markov jump systems.A new iterative algorithm is developed by using the latest estimation information and introdu... This study is concerned with the problem to solve the continuous coupled Riccati matrix equations in It?Markov jump systems.A new iterative algorithm is developed by using the latest estimation information and introducing a tuning parameter.The iterative solution obtained by the proposed algorithm with zero initial conditions converges to the unique positive definite solution of the considered equations.The convergence rate of the algorithm is dependent on the adjustable parameter.Furthermore,a numerical example is provided to show the effectiveness of the presented algorithms. 展开更多
关键词 Ito Markov jump systems coupled Riccati matrix equations iterative algorithms
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VARIATIONAL ITERATIVE ALGORITHMS IN PHOTOACOUSTIC TOMOGRAPHY WITH VARIABLE SOUND SPEED 认领 引用
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作者 Tangjie Lv Tie Zhou 《Journal of Computational Mathematics》 SCIE CSCD 2014年第5期579-600,共22页
In this paper,we investigate the adjoint equation in photoacoustic tomography with variable sound speed,and propose three variational iterative algorithms.The basic idea of these algorithms is to compute the original ... In this paper,we investigate the adjoint equation in photoacoustic tomography with variable sound speed,and propose three variational iterative algorithms.The basic idea of these algorithms is to compute the original equation and the adjoint equation iteratively.We present numerical examples and show the well performance of these variational iterative algorithms. 展开更多
关键词 Photoacoustic Tomography Variational iterative algorithms
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DDoS Attack Tracking Using Multi-Round Iterative Viterbi Algorithm in Satellite Internet 认领 引用 被引量：1
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作者 Guo Wei Xu Jin +2 位作者 Pei Yukui Yin Liuguo Feng Wei 《China Communications》 SCIE EI CSCD 2025年第3期148-163,共16页
Satellite Internet(SI)provides broadband access as a critical information infrastructure in 6G.However,with the integration of the terrestrial Internet,the influx of massive terrestrial traffic will bring significant ... Satellite Internet(SI)provides broadband access as a critical information infrastructure in 6G.However,with the integration of the terrestrial Internet,the influx of massive terrestrial traffic will bring significant threats to SI,among which DDoS attack will intensify the erosion of limited bandwidth resources.Therefore,this paper proposes a DDoS attack tracking scheme using a multi-round iterative Viterbi algorithm to achieve high-accuracy attack path reconstruction and fast internal source locking,protecting SI from the source.Firstly,to reduce communication overhead,the logarithmic representation of the traffic volume is added to the digests after modeling SI,generating the lightweight deviation degree to construct the observation probability matrix for the Viterbi algorithm.Secondly,the path node matrix is expanded to multi-index matrices in the Viterbi algorithm to store index information for all probability values,deriving the path with non-repeatability and maximum probability.Finally,multiple rounds of iterative Viterbi tracking are performed locally to track DDoS attack based on trimming tracking results.Simulation and experimental results show that the scheme can achieve 96.8%tracking accuracy of external and internal DDoS attack at 2.5 seconds,with the communication overhead at 268KB/s,effectively protecting the limited bandwidth resources of SI. 展开更多
关键词 DDoS tracking iterative Viterbi algorithm satellite Internet 6G
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MONOTONIC ITERATIVE ALGORITHMS FOR A QUASICOMPLEMENTARITY PROBLEM 认领 引用
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作者 Zhou, SZ Zan, WP Zeng, JP 《Journal of Computational Mathematics》 SCIE EI 2001年第3期293-298,共6页
Focuses on a study which presented monotonic iterative algorithms for solving quasicomplementarity problem (QCP). Details on the sequential complementarity problem (CP) algorithm; Information on the supersolution and ... Focuses on a study which presented monotonic iterative algorithms for solving quasicomplementarity problem (QCP). Details on the sequential complementarity problem (CP) algorithm; Information on the supersolution and subsolution of CP to QCP; Equation of Schwarz algorithm. 展开更多
关键词 quasicomplementarity problem iterative algorithm monotonic convergence Schwarz algorithm
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Block Monotone Iterative Algorithms for Variational Inequalities with Nonlinear Operators 认领 引用
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作者 Ming-hui Ren Jin-ping Zeng 《Acta Mathematicae Applicatae Sinica》 SCIE 2008年第2期221-232,共12页
Some block iterative methods for solving variational inequalities with nonlinear operators are proposed. Monotone convergence of the algorithms is obtained. Some comparison theorems are also established. Compared with... Some block iterative methods for solving variational inequalities with nonlinear operators are proposed. Monotone convergence of the algorithms is obtained. Some comparison theorems are also established. Compared with the research work in given by Pao in 1995 for nonlinear equations and research work in given by Zeng and Zhou in 2002 for elliptic variational inequalities, the algorithms proposed in this paper are independent of the boundedness of the derivatives of the nonlinear operator. 展开更多
关键词 Monotone iterative algorithm upper solution lower solution comparison theorem variationalinequality
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Iterative solution and numerical analysis of vehicle-track-bridge nonlinear coupled vibration considering viscoelasticity of rail pads 认领 引用
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作者 CUI Wei-tao GAO Liang +3 位作者 XIAO Hong MIAO Shuai-jie NIU Zhen-yu XIAO Yi-xiong 《Journal of Central South University》 SCIE EI CAS CSCD 2025年第7期2750-2765,共16页
To investigate the effect of rail pad viscoelasticity on vehicle-track-bridge coupled vibration,the fractional Voigt and Maxwell model in parallel(FVMP)was used to characterize the viscoelastic properties of the rail ... To investigate the effect of rail pad viscoelasticity on vehicle-track-bridge coupled vibration,the fractional Voigt and Maxwell model in parallel(FVMP)was used to characterize the viscoelastic properties of the rail pad based on dynamic performance test results.The FVMP model was then incorporated into the vehicle-track-bridge nonlinear coupled model,and its dynamic response was solved using a cross-iteration algorithm with a relaxation factor.Results indicate that the nonlinear coupled model achieves good convergence when the time step is less than 0.001 s,with the cross-iteration algorithm adjusting the wheel-rail force.In particular,the best convergence is achieved when the relaxation factor is within the range of 0.3-0.5.The FVMP model effectively characterizes the viscoelasticity of rail pads across a temperature range of±20℃and a frequency range of 1-1000 Hz.The viscoelasticity of rail pads significantly affects high-frequency vibrations in the coupled system,particularly around 50 Hz,corresponding to the wheel-rail coupled resonance range.Considering rail pad viscoelasticity is essential for accurately predicting track structure vibrations. 展开更多
关键词 high-speed railway rail pads fractional derivative vehicle-track-bridge coupled model iterative algorithm
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ON THE CONVERGENCE OF MULTIPLICATIVE ITERATIVE ALGORITHMS WITH INEXACT LINE SEARCH 认领 引用
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作者 杨晓光 《Acta Mathematicae Applicatae Sinica》 1997年第4期337-341,共5页
This paper studies thee convergence properties of multiplicative iterative algorithms with inexact line search. We prove that the convergence can be guaranteed for a general form of line search rille, under the assump... This paper studies thee convergence properties of multiplicative iterative algorithms with inexact line search. We prove that the convergence can be guaranteed for a general form of line search rille, under the assumption of convexity of objective function or the assumption of convergence of the sequence generated by the algorithm. This answers an open problem put forward by lusem. 展开更多
关键词 Multipl,icative iterative algorithm inexact line search convergence
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A lifting-wavelet-based iterative thresholding correction for atomic force microscopy images with vertical distortion 认领 引用
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作者 Yifan Bai Yinan Wu Yongchun Fang 《Nanotechnology and Precision Engineering》 EI CAS CSCD 2025年第3期29-40,共12页
To eliminate distortion caused by vertical drift and illusory slopes in atomic force microscopy(AFM)imaging,a lifting-wavelet-based iterative thresholding correction method is proposed in this paper.This method achiev... To eliminate distortion caused by vertical drift and illusory slopes in atomic force microscopy(AFM)imaging,a lifting-wavelet-based iterative thresholding correction method is proposed in this paper.This method achieves high-quality AFM imaging via line-by-line corrections for each distorted profile along the fast axis.The key to this line-by-line correction is to accurately simulate the profile distortion of each scanning row.Therefore,a data preprocessing approach is first developed to roughly filter out most of the height data that impairs the accuracy of distortion modeling.This process is implemented through an internal double-screening mechanism.A line-fitting method is adopted to preliminarily screen out the obvious specimens.Lifting wavelet analysis is then carried out to identify the base parts that are mistakenly filtered out as specimens so as to preserve most of the base profiles and provide a good basis for further distortion modeling.Next,an iterative thresholding algorithm is developed to precisely simulate the profile distortion.By utilizing the roughly screened base profile,the optimal threshold,which is used to screen out the pure bases suitable for distortion modeling,is determined through iteration with a specified error rule.On this basis,the profile distortion is accurately modeled through line fitting on the finely screened base data,and the correction is implemented by subtracting the modeling result from the distorted profile.Finally,the effectiveness of the proposed method is verified through experiments and applications. 展开更多
关键词 Atomic force microscopy Lifting wavelet analysis Iterative thresholding algorithm Vertical distortion
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Gradient Optimization Assisted Bubble Sampling Method for Structural Reliability Analysis 认领 引用
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作者 Zeng Meng LiwenjieShen +2 位作者 Changquan Li Jiaxiang Yi Gang Dong 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2026年第6期891-904,共14页
The sampling method is an important numerical technique for solving reliability problems in engineering systems.However,the evaluation of the failure probability using classical sampling methods is time-consuming for ... The sampling method is an important numerical technique for solving reliability problems in engineering systems.However,the evaluation of the failure probability using classical sampling methods is time-consuming for complex engineering structure.To address this issue,this paper proposes a gradient optimization assisted bubble sampling method(GOBSM)to reduce the computational costs,which enhances the coverage range of bubbles,thereby improving the computational efficiency without sacrificing the accuracy.Furthermore,the bubble gradient iterative algorithm is developed to efficiently construct bubbles.Eight complex numerical examples are tested for assessing the failure probability,and the results demonstrate the performance of GOBSM. 展开更多
关键词 Reliability analysis Bubble sampling method Bubble gradient iterative algorithm Failure probability
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PREDICTOR-CORRECTOR ALGORITHMS FOR SOLVING GENERALIZED MIXED IMPLICIT QUASI-EQUILIBRIUM PROBLEMS 认领 引用
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作者 丁协平 林炎诚 姚任之 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第9期1157-1164,共8页
A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems... A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi-variational inequality problems as many special cases. By employing the auxiliary principle technique, some predictor-corrector iterative algorithms for solving the GMIQEP are suggested and analyzed. The convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings 展开更多
关键词 generalized mixed implicit quasi-equilibrium problem auxiliary variational inequality predictor-corrector iterative algorithms partially relaxed implicit strong monotonicity
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An online value iteration method for stochastic linear quadratic control with multiplicative noise 认领 引用
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作者 Shumei Li Bing-Chang Wang Baoqiang Zhang 《Control Theory and Technology》 EI CSCD 2026年第3期451-461,共11页
This paper proposes a model-free online value iteration(VI)algorithm for solving stochastic linear quadratic control problems with ergodic cost functions,where the diffusion term in the dynamics equation is influenced... This paper proposes a model-free online value iteration(VI)algorithm for solving stochastic linear quadratic control problems with ergodic cost functions,where the diffusion term in the dynamics equation is influenced by both the state and control variables.First,we propose an offline VI algorithm based on the idea of stochastic approximation.However,this algorithm requires prior knowledge of the system parameters,which are not always readily available.To overcome this limitation,we then develop a(partially)model-free online learning algorithm based on VI.This algorithm only requires a single system trajectory and does not need the initial control to be stabilizing.By exploiting the growth rate of Itô’s integrals to handle the stochastic term generated by multiplicative noise,we provide a rigorous proof of the algorithm’s convergence.Finally,a simulation example is presented to validate the convergence of the proposed algorithms. 展开更多
关键词 Stochastic linear quadratic problem Model-free Value iteration algorithm Ergodic control Robust dynamic programming
An Interpretable Temporal Convolutional Framework for Granger Causality Analysis 认领 引用
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作者 Aoxiang Dong Andrew Starr Yifan Zhao 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2026年第3期665-679,共15页
Most existing parametric approaches for detecting linear or nonlinear Granger causality(GC)face challenges in estimating appropriate time delays,a critical factor for accurate GC detection.This issue becomes particula... Most existing parametric approaches for detecting linear or nonlinear Granger causality(GC)face challenges in estimating appropriate time delays,a critical factor for accurate GC detection.This issue becomes particularly pronounced in nonlinear complex systems,which are often opaque and consist of numerous components or variables.In this paper,we propose a novel temporal convolutional network(TCN)-based end-to-end GC detection approach called the interpretable temporal convolutional framework(ITCF).Unlike conventional deep learning models,which act like a“black box”and are difficult to analyse the interactions between variables,the proposed ITCF is able to detect both linear and nonlinear GC and automatically estimate time delay during the multivariant time series prediction.Specifically,GC is obtained by employing the least absolute shrinkage and selection operator(Lasso)regression during the prediction of multivariate time series using TCN.Then,time delays can be estimated by interpreting the TCN kernels.We propose a convolutional hierarchical group Lasso(cHGL),a hierarchical regularisation approach to effectively utilise temporal information within each TCN channel for enhanced GC detection.Additionally,as far as we are concerned,this paper is the first to integrate the Iterative Soft-Thresholding Algorithm into the backpropagation of TCN to optimise the proposed cHGL,which enables causal channel selection and induces sparsity within each TCN channel to remove redundant temporal information,ultimately creating an end-to-end GC detection framework.The testing results of four experiments,involving two simulations and two real data,demonstrate that the proposed ITCF,in comparison with state-ofthe-art,offers a more reliable estimation of GC relationships in complex systems featuring intricate dynamics,limited data lengths,or numerous variables. 展开更多
关键词 Granger causality(GC) interpretable deep learning iterative soft-thresholding algorithm(ISTA) least absolute shrinkage and selection operator(Lasso) temporal convolutional network(TCN)
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Geometrically Nonlinear Deformation Reconstruction Based on iQS4 Elements Using a Linearized Iterative iFEM Algorithm 认领 引用 被引量：4
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作者 Mengying Li Dawei Jia +2 位作者 He Huang Ziyan Wu Adnan Kefal 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2023年第1期166-180,共15页
Structural shape monitoring plays a vital role in the structural health monitoring systems.The inverse finite element method(iFEM)has been demonstrated to be a practical method of deformation reconstruction owing to i... Structural shape monitoring plays a vital role in the structural health monitoring systems.The inverse finite element method(iFEM)has been demonstrated to be a practical method of deformation reconstruction owing to its unique advantages.Current iFEM formulations have been applied to small deformation of structures based on the small-displacement assumption of linear theory.However,this assumption may be inapplicable to some structures with large displacements in practical applications.Therefore,geometric nonlinearity needs to be considered.In this study,to expand the practical utility of iFEM for large displacement monitoring,we propose a nonlinear iFEM algorithm based on a four-node inverse quadrilateral shell element iQS4.Taking the advantage of an iterative iFEM algorithm,a nonlinear response is linearized to compute the geometrically nonlinear deformation reconstruction,like the basic concept of nonlinear FE analysis.Several examples are solved to verify the proposed approach.It is demonstrated that large displacements can be accurately estimated even if the in-situ sensor data includes different levels of randomly generated noise.It is proven that the nonlinear iFEM algorithm provides a more accurate displacement response as compared to the linear iFEM methodology for structures undergoing large displacement.Hence,the proposed approach can be utilized as a viable tool to effectively characterize geometrically nonlinear deformations of structures in real-time applications. 展开更多
关键词 Deformation reconstruction iQS4 element Iterative algorithm Nonlinear iFEM Geometric nonlinearity
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