Failure detection is an essential task in industrial systems for preventing costly downtime and ensuring the seamlessoperation of the system. Current industrial processes are getting smarter with the emergence of Indu...Failure detection is an essential task in industrial systems for preventing costly downtime and ensuring the seamlessoperation of the system. Current industrial processes are getting smarter with the emergence of Industry 4.0.Specifically, various modernized industrial processes have been equipped with quite a few sensors to collectprocess-based data to find faults arising or prevailing in processes along with monitoring the status of processes.Fault diagnosis of rotating machines serves a main role in the engineering field and industrial production. Dueto the disadvantages of existing fault, diagnosis approaches, which greatly depend on professional experienceand human knowledge, intellectual fault diagnosis based on deep learning (DL) has attracted the researcher’sinterest. DL reaches the desired fault classification and automatic feature learning. Therefore, this article designs a Gradient Optimizer Algorithm with Hybrid Deep Learning-based Failure Detection and Classification (GOAHDLFDC)in the industrial environment. The presented GOAHDL-FDC technique initially applies continuous wavelettransform (CWT) for preprocessing the actual vibrational signals of the rotating machinery. Next, the residualnetwork (ResNet18) model was exploited for the extraction of features from the vibration signals which are thenfed into theHDLmodel for automated fault detection. Finally, theGOA-based hyperparameter tuning is performedtoadjust the parameter valuesof theHDLmodel accurately.The experimental result analysis of the GOAHDL-FD Calgorithm takes place using a series of simulations and the experimentation outcomes highlight the better resultsof the GOAHDL-FDC technique under different aspects.展开更多
A subspace projected conjugate gradient method is proposed for solving large bound constrained quadratic programming. The conjugate gradient method is used to update the variables with indices outside of the active se...A subspace projected conjugate gradient method is proposed for solving large bound constrained quadratic programming. The conjugate gradient method is used to update the variables with indices outside of the active set, while the projected gradient method is used to update the active variables. At every iterative level, the search direction consists of two parts, one of which is a subspace trumcated Newton direction, another is a modified gradient direction. With the projected search the algorithm is suitable to large problems. The convergence of the method is proved and same numerical tests with dimensions ranging from 5000 to 20000 are given.展开更多
Large-scale multi-objective optimization problems(LSMOPs)pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces.While evolutionary algorithms a...Large-scale multi-objective optimization problems(LSMOPs)pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces.While evolutionary algorithms are good at solving small-scale multi-objective optimization problems,they are criticized for low efficiency in converging to the optimums of LSMOPs.By contrast,mathematical programming methods offer fast convergence speed on large-scale single-objective optimization problems,but they have difficulties in finding diverse solutions for LSMOPs.Currently,how to integrate evolutionary algorithms with mathematical programming methods to solve LSMOPs remains unexplored.In this paper,a hybrid algorithm is tailored for LSMOPs by coupling differential evolution and a conjugate gradient method.On the one hand,conjugate gradients and differential evolution are used to update different decision variables of a set of solutions,where the former drives the solutions to quickly converge towards the Pareto front and the latter promotes the diversity of the solutions to cover the whole Pareto front.On the other hand,objective decomposition strategy of evolutionary multi-objective optimization is used to differentiate the conjugate gradients of solutions,and the line search strategy of mathematical programming is used to ensure the higher quality of each offspring than its parent.In comparison with state-of-the-art evolutionary algorithms,mathematical programming methods,and hybrid algorithms,the proposed algorithm exhibits better convergence and diversity performance on a variety of benchmark and real-world LSMOPs.展开更多
The fast convergence without initial value dependence is the key to solving large angle relative orientation.Therefore,a hybrid conjugate gradient algorithm is proposed in this paper.The concrete process is:①stochast...The fast convergence without initial value dependence is the key to solving large angle relative orientation.Therefore,a hybrid conjugate gradient algorithm is proposed in this paper.The concrete process is:①stochastic hill climbing(SHC)algorithm is used to make a random disturbance to the given initial value of the relative orientation element,and the new value to guarantee the optimization direction is generated.②In local optimization,a super-linear convergent conjugate gradient method is used to replace the steepest descent method in relative orientation to improve its convergence rate.③The global convergence condition is that the calculation error is less than the prescribed limit error.The comparison experiment shows that the method proposed in this paper is independent of the initial value,and has higher accuracy and fewer iterations.展开更多
This paper designs a 3 mm radiometer and validate with experiments based on the principle of passive millimeter wave (PMMW) imaging. The poor spatial resolution, which is limited by antenna size, should be improved ...This paper designs a 3 mm radiometer and validate with experiments based on the principle of passive millimeter wave (PMMW) imaging. The poor spatial resolution, which is limited by antenna size, should be improved by post data processing. A conjugate-gradient (CG) algorithm is adopted to circumvent this drawback. Simulation and real data collected in laboratory environment are given, and the results show that the CG algorithm improves the spatial resolution and convergent rate. Further, it can reduce the ringing effects which are caused by regularizing the image restoration. Thus, the CG algorithm is easily implemented for PMMW imaging.展开更多
The dropping off of data during information transmission and the storage device’s damage etc.often leads the sampled data to be non-uniform.The paper, based on the stability theory of irregular wavelet frame and the ...The dropping off of data during information transmission and the storage device’s damage etc.often leads the sampled data to be non-uniform.The paper, based on the stability theory of irregular wavelet frame and the irregular weighted wavelet frame operator,proposed an irregular weighted wavelet fame conjugate gradient iterative algorithm for the reconstruction of non-uniformly sampling signal. Compared the experiment results with the iterative algorithm of the Ref.[5],the new algorithm has remarkable advantages in approximation error,running time and so on.展开更多
For unachievable tracking problems, where the system output cannot precisely track a given reference, achieving the best possible approximation for the reference trajectory becomes the objective. This study aims to in...For unachievable tracking problems, where the system output cannot precisely track a given reference, achieving the best possible approximation for the reference trajectory becomes the objective. This study aims to investigate solutions using the Ptype learning control scheme. Initially, we demonstrate the necessity of gradient information for achieving the best approximation.Subsequently, we propose an input-output-driven learning gain design to handle the imprecise gradients of a class of uncertain systems. However, it is discovered that the desired performance may not be attainable when faced with incomplete information.To address this issue, an extended iterative learning control scheme is introduced. In this scheme, the tracking errors are modified through output data sampling, which incorporates lowmemory footprints and offers flexibility in learning gain design.The input sequence is shown to converge towards the desired input, resulting in an output that is closest to the given reference in the least square sense. Numerical simulations are provided to validate the theoretical findings.展开更多
This paper proposed a new normalized transform domain conjugate gradient algorithm (NT-CGA), which applies the data independent normalized orthogonal transform technique to approximately whiten the input signal and ut...This paper proposed a new normalized transform domain conjugate gradient algorithm (NT-CGA), which applies the data independent normalized orthogonal transform technique to approximately whiten the input signal and utilises the modified conjugate gradient method to perform sample-by-sample updating of the filter weights more efficiently. Simulation results illustrated that the proposed algorithm has the ability to provide a fast convergence speed and lower steady-error compared to that of traditional least mean square algorithm (LMSA), normalized transform domain least mean square algorithm (NT- LMSA), Quasi-Newton least mean square algorithm (Q-LMSA) and time domain conjugate gradient algorithm (TD-CGA) when the input signal is heavily coloured.展开更多
Two new formulaes of the main parameter βk of the conjugate gradient method are presented, which respectively can be seen as the modifications of method HS and PRP. In comparison with classic conjugate gradient metho...Two new formulaes of the main parameter βk of the conjugate gradient method are presented, which respectively can be seen as the modifications of method HS and PRP. In comparison with classic conjugate gradient methods, the new methods take both available gradient and function value information. Furthermore, their modifications are proposed. These methods are shown to be global convergent under some assumptions. Numerical results are also reported.展开更多
With the increasing prevalence of high-order systems in engineering applications, these systems often exhibitsignificant disturbances and can be challenging to model accurately. As a result, the active disturbance rej...With the increasing prevalence of high-order systems in engineering applications, these systems often exhibitsignificant disturbances and can be challenging to model accurately. As a result, the active disturbance rejectioncontroller (ADRC) has been widely applied in various fields. However, in controlling plant protection unmannedaerial vehicles (UAVs), which are typically large and subject to significant disturbances, load disturbances andthe possibility of multiple actuator faults during pesticide spraying pose significant challenges. To address theseissues, this paper proposes a novel fault-tolerant control method that combines a radial basis function neuralnetwork (RBFNN) with a second-order ADRC and leverages a fractional gradient descent (FGD) algorithm.We integrate the plant protection UAV model’s uncertain parameters, load disturbance parameters, and actuatorfault parameters and utilize the RBFNN for system parameter identification. The resulting ADRC exhibits loaddisturbance suppression and fault tolerance capabilities, and our proposed active fault-tolerant control law hasLyapunov stability implications. Experimental results obtained using a multi-rotor fault-tolerant test platformdemonstrate that the proposed method outperforms other control strategies regarding load disturbance suppressionand fault-tolerant performance.展开更多
This paper discusses a special class of mathematical programs with equilibrium constraints. At first, by using a generalized complementarity function, the discussed problem is transformed into a family of general nonl...This paper discusses a special class of mathematical programs with equilibrium constraints. At first, by using a generalized complementarity function, the discussed problem is transformed into a family of general nonlinear optimization problems containing additional variable μ. Furthermore, combining the idea of penalty function, an auxiliary problem with inequality constraints is presented. And then, by providing explicit searching direction, we establish a new conjugate projection gradient method for optimization with nonlinear complementarity constraints. Under some suitable conditions, the proposed method is proved to possess global and superlinear convergence rate.展开更多
It is well known that Newton and quasi-Newton algorithms are effective to small and medium scale smooth problems because they take full use of corresponding gradient function’s information but fail to solve nonsmooth...It is well known that Newton and quasi-Newton algorithms are effective to small and medium scale smooth problems because they take full use of corresponding gradient function’s information but fail to solve nonsmooth problems.The perfect algorithm stems from concept of‘bundle’successfully addresses both smooth and nonsmooth complex problems,but it is regrettable that it is merely effective to small and medium optimization models since it needs to store and update relevant information of parameter’s bundle.The conjugate gradient algorithm is effective both large-scale smooth and nonsmooth optimization model since its simplicity that utilizes objective function’s information and the technique of Moreau-Yosida regularization.Thus,a modified three-term conjugate gradient algorithm was proposed,and it has a sufficiently descent property and a trust region character.At the same time,it possesses the global convergence under mild assumptions and numerical test proves it is efficient than similar optimization algorithms.展开更多
In this paper, we present a new hybrid conjugate gradient algorithm for unconstrained optimization. This method is a convex combination of Liu-Storey conjugate gradient method and Fletcher-Reeves conjugate gradient me...In this paper, we present a new hybrid conjugate gradient algorithm for unconstrained optimization. This method is a convex combination of Liu-Storey conjugate gradient method and Fletcher-Reeves conjugate gradient method. We also prove that the search direction of any hybrid conjugate gradient method, which is a convex combination of two conjugate gradient methods, satisfies the famous D-L conjugacy condition and in the same time accords with the Newton direction with the suitable condition. Furthermore, this property doesn't depend on any line search. Next, we also prove that, moduling the value of the parameter t,the Newton direction condition is equivalent to Dai-Liao conjugacy condition.The strong Wolfe line search conditions are used.The global convergence of this new method is proved.Numerical comparisons show that the present hybrid conjugate gradient algorithm is the efficient one.展开更多
Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering (CAE) and computer aided manufacturing ...Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering (CAE) and computer aided manufacturing (CAM). This paper presents a high-efficiency improved symmetric successive over-relaxation (ISSOR) preconditioned conjugate gradient (PCG) method, which maintains lelism consistent with the original form. Ideally, the by 50% as compared with the original algorithm. the convergence and inherent paralcomputation can It is suitable for be reduced nearly high-performance computing with its inherent basic high-efficiency operations. By comparing with the numerical results, it is shown that the proposed method has the best performance.展开更多
基于阻抗张肌数据, tipper 数据,和conjugate 坡度算法的分析,我们发展一三维( 3D )为转换结合坡度算法完整的信息数据决定了从的 magnetotelluric 五电并且磁场部件并且讨论方法为 3D 倒置结果的量的解释使用完整的信息数据。从合...基于阻抗张肌数据, tipper 数据,和conjugate 坡度算法的分析,我们发展一三维( 3D )为转换结合坡度算法完整的信息数据决定了从的 magnetotelluric 五电并且磁场部件并且讨论方法为 3D 倒置结果的量的解释使用完整的信息数据。从合成数据的 3D 倒置的结果显示从转换的结果更好联合张肌和 tipper 数据是的阻抗比的完整的信息数据源于转换仅仅阻抗张肌数据(或 tipper 数据) 在改进分辨率和可靠性。合成例子也表明这个 3D 倒置算法的有效性和稳定性。展开更多
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
In this paper, we propose a globally convergent Polak-Ribiere-Polyak (PRP) conjugate gradient method for nonconvex minimization of differentiable functions by employing an Armijo-type line search which is simpler and ...In this paper, we propose a globally convergent Polak-Ribiere-Polyak (PRP) conjugate gradient method for nonconvex minimization of differentiable functions by employing an Armijo-type line search which is simpler and less demanding than those defined in [4,10]. A favorite property of this method is that we can choose the initial stepsize as the one-dimensional minimizer of a quadratic modelΦ(t):= f(xk)+tgkTdk+(1/2) t2dkTQkdk, where Qk is a positive definite matrix that carries some second order information of the objective function f. So, this line search may make the stepsize tk more easily accepted. Preliminary numerical results show that this method is efficient.展开更多
基金The Deanship of Scientific Research(DSR)at King Abdulaziz University(KAU),Jeddah,Saudi Arabia has funded this project under Grant No.(G:651-135-1443).
文摘Failure detection is an essential task in industrial systems for preventing costly downtime and ensuring the seamlessoperation of the system. Current industrial processes are getting smarter with the emergence of Industry 4.0.Specifically, various modernized industrial processes have been equipped with quite a few sensors to collectprocess-based data to find faults arising or prevailing in processes along with monitoring the status of processes.Fault diagnosis of rotating machines serves a main role in the engineering field and industrial production. Dueto the disadvantages of existing fault, diagnosis approaches, which greatly depend on professional experienceand human knowledge, intellectual fault diagnosis based on deep learning (DL) has attracted the researcher’sinterest. DL reaches the desired fault classification and automatic feature learning. Therefore, this article designs a Gradient Optimizer Algorithm with Hybrid Deep Learning-based Failure Detection and Classification (GOAHDLFDC)in the industrial environment. The presented GOAHDL-FDC technique initially applies continuous wavelettransform (CWT) for preprocessing the actual vibrational signals of the rotating machinery. Next, the residualnetwork (ResNet18) model was exploited for the extraction of features from the vibration signals which are thenfed into theHDLmodel for automated fault detection. Finally, theGOA-based hyperparameter tuning is performedtoadjust the parameter valuesof theHDLmodel accurately.The experimental result analysis of the GOAHDL-FD Calgorithm takes place using a series of simulations and the experimentation outcomes highlight the better resultsof the GOAHDL-FDC technique under different aspects.
基金This research was supported by Chinese NNSF grant and NSF grant of Jiangsu Province
文摘A subspace projected conjugate gradient method is proposed for solving large bound constrained quadratic programming. The conjugate gradient method is used to update the variables with indices outside of the active set, while the projected gradient method is used to update the active variables. At every iterative level, the search direction consists of two parts, one of which is a subspace trumcated Newton direction, another is a modified gradient direction. With the projected search the algorithm is suitable to large problems. The convergence of the method is proved and same numerical tests with dimensions ranging from 5000 to 20000 are given.
基金supported in part by the National Key Research and Development Program of China(2018AAA0100100)the National Natural Science Foundation of China(61906001,62136008,U21A20512)+1 种基金the Key Program of Natural Science Project of Educational Commission of Anhui Province(KJ2020A0036)Alexander von Humboldt Professorship for Artificial Intelligence Funded by the Federal Ministry of Education and Research,Germany。
文摘Large-scale multi-objective optimization problems(LSMOPs)pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces.While evolutionary algorithms are good at solving small-scale multi-objective optimization problems,they are criticized for low efficiency in converging to the optimums of LSMOPs.By contrast,mathematical programming methods offer fast convergence speed on large-scale single-objective optimization problems,but they have difficulties in finding diverse solutions for LSMOPs.Currently,how to integrate evolutionary algorithms with mathematical programming methods to solve LSMOPs remains unexplored.In this paper,a hybrid algorithm is tailored for LSMOPs by coupling differential evolution and a conjugate gradient method.On the one hand,conjugate gradients and differential evolution are used to update different decision variables of a set of solutions,where the former drives the solutions to quickly converge towards the Pareto front and the latter promotes the diversity of the solutions to cover the whole Pareto front.On the other hand,objective decomposition strategy of evolutionary multi-objective optimization is used to differentiate the conjugate gradients of solutions,and the line search strategy of mathematical programming is used to ensure the higher quality of each offspring than its parent.In comparison with state-of-the-art evolutionary algorithms,mathematical programming methods,and hybrid algorithms,the proposed algorithm exhibits better convergence and diversity performance on a variety of benchmark and real-world LSMOPs.
基金National Natural Science Foundation of China(Nos.4156108241161061)。
文摘The fast convergence without initial value dependence is the key to solving large angle relative orientation.Therefore,a hybrid conjugate gradient algorithm is proposed in this paper.The concrete process is:①stochastic hill climbing(SHC)algorithm is used to make a random disturbance to the given initial value of the relative orientation element,and the new value to guarantee the optimization direction is generated.②In local optimization,a super-linear convergent conjugate gradient method is used to replace the steepest descent method in relative orientation to improve its convergence rate.③The global convergence condition is that the calculation error is less than the prescribed limit error.The comparison experiment shows that the method proposed in this paper is independent of the initial value,and has higher accuracy and fewer iterations.
基金supported partly by the State Key Program of National Natural Science Foundation of China(60632020)the Youth Science Foundation of University of Electronic Science and Technology of China(JX0823).
文摘This paper designs a 3 mm radiometer and validate with experiments based on the principle of passive millimeter wave (PMMW) imaging. The poor spatial resolution, which is limited by antenna size, should be improved by post data processing. A conjugate-gradient (CG) algorithm is adopted to circumvent this drawback. Simulation and real data collected in laboratory environment are given, and the results show that the CG algorithm improves the spatial resolution and convergent rate. Further, it can reduce the ringing effects which are caused by regularizing the image restoration. Thus, the CG algorithm is easily implemented for PMMW imaging.
基金supported by Hunan Education Office Foundation under Grant 06C260
文摘The dropping off of data during information transmission and the storage device’s damage etc.often leads the sampled data to be non-uniform.The paper, based on the stability theory of irregular wavelet frame and the irregular weighted wavelet frame operator,proposed an irregular weighted wavelet fame conjugate gradient iterative algorithm for the reconstruction of non-uniformly sampling signal. Compared the experiment results with the iterative algorithm of the Ref.[5],the new algorithm has remarkable advantages in approximation error,running time and so on.
基金supported by the National Natural Science Foundation of China (62173333, 12271522)Beijing Natural Science Foundation (Z210002)the Research Fund of Renmin University of China (2021030187)。
文摘For unachievable tracking problems, where the system output cannot precisely track a given reference, achieving the best possible approximation for the reference trajectory becomes the objective. This study aims to investigate solutions using the Ptype learning control scheme. Initially, we demonstrate the necessity of gradient information for achieving the best approximation.Subsequently, we propose an input-output-driven learning gain design to handle the imprecise gradients of a class of uncertain systems. However, it is discovered that the desired performance may not be attainable when faced with incomplete information.To address this issue, an extended iterative learning control scheme is introduced. In this scheme, the tracking errors are modified through output data sampling, which incorporates lowmemory footprints and offers flexibility in learning gain design.The input sequence is shown to converge towards the desired input, resulting in an output that is closest to the given reference in the least square sense. Numerical simulations are provided to validate the theoretical findings.
文摘This paper proposed a new normalized transform domain conjugate gradient algorithm (NT-CGA), which applies the data independent normalized orthogonal transform technique to approximately whiten the input signal and utilises the modified conjugate gradient method to perform sample-by-sample updating of the filter weights more efficiently. Simulation results illustrated that the proposed algorithm has the ability to provide a fast convergence speed and lower steady-error compared to that of traditional least mean square algorithm (LMSA), normalized transform domain least mean square algorithm (NT- LMSA), Quasi-Newton least mean square algorithm (Q-LMSA) and time domain conjugate gradient algorithm (TD-CGA) when the input signal is heavily coloured.
基金supported by the Teaching and Research Award Program for the Outstanding Young Teachers in Higher Education Institutesof Ministry of Educationthe Natural Science Foundation of Inner Mongolia Autonomous Region (2010BS0108)SPH-IMU (Z20090135)
文摘Two new formulaes of the main parameter βk of the conjugate gradient method are presented, which respectively can be seen as the modifications of method HS and PRP. In comparison with classic conjugate gradient methods, the new methods take both available gradient and function value information. Furthermore, their modifications are proposed. These methods are shown to be global convergent under some assumptions. Numerical results are also reported.
基金the 2021 Key Project of Natural Science and Technology of Yangzhou Polytechnic Institute,Active Disturbance Rejection and Fault-Tolerant Control of Multi-Rotor Plant ProtectionUAV Based on QBall-X4(Grant Number 2021xjzk002).
文摘With the increasing prevalence of high-order systems in engineering applications, these systems often exhibitsignificant disturbances and can be challenging to model accurately. As a result, the active disturbance rejectioncontroller (ADRC) has been widely applied in various fields. However, in controlling plant protection unmannedaerial vehicles (UAVs), which are typically large and subject to significant disturbances, load disturbances andthe possibility of multiple actuator faults during pesticide spraying pose significant challenges. To address theseissues, this paper proposes a novel fault-tolerant control method that combines a radial basis function neuralnetwork (RBFNN) with a second-order ADRC and leverages a fractional gradient descent (FGD) algorithm.We integrate the plant protection UAV model’s uncertain parameters, load disturbance parameters, and actuatorfault parameters and utilize the RBFNN for system parameter identification. The resulting ADRC exhibits loaddisturbance suppression and fault tolerance capabilities, and our proposed active fault-tolerant control law hasLyapunov stability implications. Experimental results obtained using a multi-rotor fault-tolerant test platformdemonstrate that the proposed method outperforms other control strategies regarding load disturbance suppressionand fault-tolerant performance.
文摘This paper discusses a special class of mathematical programs with equilibrium constraints. At first, by using a generalized complementarity function, the discussed problem is transformed into a family of general nonlinear optimization problems containing additional variable μ. Furthermore, combining the idea of penalty function, an auxiliary problem with inequality constraints is presented. And then, by providing explicit searching direction, we establish a new conjugate projection gradient method for optimization with nonlinear complementarity constraints. Under some suitable conditions, the proposed method is proved to possess global and superlinear convergence rate.
基金This work is supported by the National Natural Science Foundation of China(Grant No.11661009)the Guangxi Science Fund for Distinguished Young Scholars(No.2015GXNSFGA139001)+1 种基金the Guangxi Natural Science Key Fund(No.2017GXNSFDA198046)Innovation Project of Guangxi Graduate Education(No.YCSW2018046).
文摘It is well known that Newton and quasi-Newton algorithms are effective to small and medium scale smooth problems because they take full use of corresponding gradient function’s information but fail to solve nonsmooth problems.The perfect algorithm stems from concept of‘bundle’successfully addresses both smooth and nonsmooth complex problems,but it is regrettable that it is merely effective to small and medium optimization models since it needs to store and update relevant information of parameter’s bundle.The conjugate gradient algorithm is effective both large-scale smooth and nonsmooth optimization model since its simplicity that utilizes objective function’s information and the technique of Moreau-Yosida regularization.Thus,a modified three-term conjugate gradient algorithm was proposed,and it has a sufficiently descent property and a trust region character.At the same time,it possesses the global convergence under mild assumptions and numerical test proves it is efficient than similar optimization algorithms.
文摘In this paper, we present a new hybrid conjugate gradient algorithm for unconstrained optimization. This method is a convex combination of Liu-Storey conjugate gradient method and Fletcher-Reeves conjugate gradient method. We also prove that the search direction of any hybrid conjugate gradient method, which is a convex combination of two conjugate gradient methods, satisfies the famous D-L conjugacy condition and in the same time accords with the Newton direction with the suitable condition. Furthermore, this property doesn't depend on any line search. Next, we also prove that, moduling the value of the parameter t,the Newton direction condition is equivalent to Dai-Liao conjugacy condition.The strong Wolfe line search conditions are used.The global convergence of this new method is proved.Numerical comparisons show that the present hybrid conjugate gradient algorithm is the efficient one.
基金Project supported by the National Natural Science Foundation of China(Nos.5130926141030747+3 种基金41102181and 51121005)the National Basic Research Program of China(973 Program)(No.2011CB013503)the Young Teachers’ Initial Funding Scheme of Sun Yat-sen University(No.39000-1188140)
文摘Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering (CAE) and computer aided manufacturing (CAM). This paper presents a high-efficiency improved symmetric successive over-relaxation (ISSOR) preconditioned conjugate gradient (PCG) method, which maintains lelism consistent with the original form. Ideally, the by 50% as compared with the original algorithm. the convergence and inherent paralcomputation can It is suitable for be reduced nearly high-performance computing with its inherent basic high-efficiency operations. By comparing with the numerical results, it is shown that the proposed method has the best performance.
基金supported by the National Hi-tech Research and Development Program of China(863Program)(No.2007AA09Z310) National Natural Science Foundation of China(Grant No.40774029 40374024)+1 种基金 the Fundamental Research Funds for the Central Universities(Grant No.2010ZY53) the Program for New Century Excellent Talents in University(NCET)
文摘基于阻抗张肌数据, tipper 数据,和conjugate 坡度算法的分析,我们发展一三维( 3D )为转换结合坡度算法完整的信息数据决定了从的 magnetotelluric 五电并且磁场部件并且讨论方法为 3D 倒置结果的量的解释使用完整的信息数据。从合成数据的 3D 倒置的结果显示从转换的结果更好联合张肌和 tipper 数据是的阻抗比的完整的信息数据源于转换仅仅阻抗张肌数据(或 tipper 数据) 在改进分辨率和可靠性。合成例子也表明这个 3D 倒置算法的有效性和稳定性。
基金Project supported by the National Natural Science Foundation of China (Grant No.10271074), and the Special Funds for Major Specialities of Shanghai Education Commission (Grant No.J50101)
文摘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.
基金This work is supported by the Chinese NSF grants 60475042 Guangxi NSF grants 0542043the Foundation of Advanced Research Center of Zhongshan University and Hong Kong
文摘In this paper, we propose a globally convergent Polak-Ribiere-Polyak (PRP) conjugate gradient method for nonconvex minimization of differentiable functions by employing an Armijo-type line search which is simpler and less demanding than those defined in [4,10]. A favorite property of this method is that we can choose the initial stepsize as the one-dimensional minimizer of a quadratic modelΦ(t):= f(xk)+tgkTdk+(1/2) t2dkTQkdk, where Qk is a positive definite matrix that carries some second order information of the objective function f. So, this line search may make the stepsize tk more easily accepted. Preliminary numerical results show that this method is efficient.