Some properties of a class of quasi-differentiable functions（the difference of two finite convex functions） are considered in this paper. And the convergence of the steepest descent algorithm for unconstrained and c...Some properties of a class of quasi-differentiable functions（the difference of two finite convex functions） are considered in this paper. And the convergence of the steepest descent algorithm for unconstrained and constrained quasi-differentiable programming is proved.展开更多
A gradient descent algorithm with adjustable parameter for attitude estimation is developed,aiming at the attitude measurement for small unmanned aerial vehicle(UAV)in real-time flight conditions.The accelerometer and...A gradient descent algorithm with adjustable parameter for attitude estimation is developed,aiming at the attitude measurement for small unmanned aerial vehicle(UAV)in real-time flight conditions.The accelerometer and magnetometer are introduced to construct an error equation with the gyros,thus the drifting characteristics of gyroscope can be compensated by solving the error equation utilized by the gradient descent algorithm.Performance of the presented algorithm is evaluated using a self-proposed micro-electro-mechanical system(MEMS)based attitude heading reference system which is mounted on a tri-axis turntable.The on-ground,turntable and flight experiments indicate that the estimation attitude has a good accuracy.Also,the presented system is compared with an open-source flight control system which runs extended Kalman filter(EKF),and the results show that the attitude control system using the gradient descent method can estimate the attitudes for UAV effectively.展开更多
Under some assumptions, the solution set of a nonlinear complementarity problem coincides with the set of local minima of the corresponding minimization problem. This paper uses a family of new merit functions to deal...Under some assumptions, the solution set of a nonlinear complementarity problem coincides with the set of local minima of the corresponding minimization problem. This paper uses a family of new merit functions to deal with nonlinear complementarity problem where the underlying function is assumed to be a continuous but not necessarily locally Lipschitzian map and gives a descent algorithm for solving the nonsmooth continuous complementarity problems. In addition, the global convergence of the derivative free descent algorithm is also proved.展开更多
The gradient descent approach is the key ingredient in variational quantum algorithms and machine learning tasks,which is an optimization algorithm for finding a local minimum of an objective function.The quantum vers...The gradient descent approach is the key ingredient in variational quantum algorithms and machine learning tasks,which is an optimization algorithm for finding a local minimum of an objective function.The quantum versions of gradient descent have been investigated and implemented in calculating molecular ground states and optimizing polynomial functions.Based on the quantum gradient descent algorithm and Choi-Jamiolkowski isomorphism,we present approaches to simulate efficiently the nonequilibrium steady states of Markovian open quantum many-body systems.Two strategies are developed to evaluate the expectation values of physical observables on the nonequilibrium steady states.Moreover,we adapt the quantum gradient descent algorithm to solve linear algebra problems including linear systems of equations and matrix-vector multiplications,by converting these algebraic problems into the simulations of closed quantum systems with well-defined Hamiltonians.Detailed examples are given to test numerically the effectiveness of the proposed algorithms for the dissipative quantum transverse Ising models and matrix-vector multiplications.展开更多
In this paper,the authors propose a novel smoothing descent type algorithm with extrapolation for solving a class of constrained nonsmooth and nonconvex problems,where the nonconvex term is possibly nonsmooth.Their al...In this paper,the authors propose a novel smoothing descent type algorithm with extrapolation for solving a class of constrained nonsmooth and nonconvex problems,where the nonconvex term is possibly nonsmooth.Their algorithm adopts the proximal gradient algorithm with extrapolation and a safe-guarding policy to minimize the smoothed objective function for better practical and theoretical performance.Moreover,the algorithm uses a easily checking rule to update the smoothing parameter to ensure that any accumulation point of the generated sequence is an(afne-scaled)Clarke stationary point of the original nonsmooth and nonconvex problem.Their experimental results indicate the effectiveness of the proposed algorithm.展开更多
In this paper, we give a descent algorithm for solving quadratic bilevel programming problems. It is proved that the descent algorithm finds a locally optimal solution to a quadratic bilevel programming problem in a ...In this paper, we give a descent algorithm for solving quadratic bilevel programming problems. It is proved that the descent algorithm finds a locally optimal solution to a quadratic bilevel programming problem in a finite number of iterations. Two numerical examples are given to illustrate this algorithm.展开更多
In the field of calculating the attack area of air-to-air missiles in modern air combat scenarios,the limitations of existing research,including real-time calculation,accuracy efficiency trade-off,and the absence of t...In the field of calculating the attack area of air-to-air missiles in modern air combat scenarios,the limitations of existing research,including real-time calculation,accuracy efficiency trade-off,and the absence of the three-dimensional attack area model,restrict their practical applications.To address these issues,an improved backtracking algorithm is proposed to improve calculation efficiency.A significant reduction in solution time and maintenance of accuracy in the three-dimensional attack area are achieved by using the proposed algorithm.Furthermore,the age-layered population structure genetic programming(ALPS-GP)algorithm is introduced to determine an analytical polynomial model of the three-dimensional attack area,considering real-time requirements.The accuracy of the polynomial model is enhanced through the coefficient correction using an improved gradient descent algorithm.The study reveals a remarkable combination of high accuracy and efficient real-time computation,with a mean error of 91.89 m using the analytical polynomial model of the three-dimensional attack area solved in just 10^(-4)s,thus meeting the requirements of real-time combat scenarios.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
A large number of sparse signal reconstruction algorithms have been continuously proposed, but almost all greedy algorithms add a fixed number of indices to the support set in each iteration. Although the mechanism of...A large number of sparse signal reconstruction algorithms have been continuously proposed, but almost all greedy algorithms add a fixed number of indices to the support set in each iteration. Although the mechanism of selecting the fixed number of indexes improves the reconstruction efficiency, it also brings the problem of low index selection accuracy. Based on the full study of the theory of compressed sensing, we propose a dynamic indexes selection strategy based on residual update to improve the performance of the compressed sampling matching pursuit algorithm (CoSaMP). As an extension of CoSaMP algorithm, the proposed algorithm adopts a residual comparison strategy to improve the accuracy of backtracking selected indexes. This backtracking strategy can efficiently select backtracking indexes. And without increasing the computational complexity, the proposed improvement algorithm has a higher exact reconstruction rate and peak signal to noise ratio (PSNR). Simulation results demonstrate the proposed algorithm significantly outperforms the CoSaMP for image recovery and one-dimensional signal.展开更多
With the development of the compressive sensing theory, the image reconstruction from the projections viewed in limited angles is one of the hot problems in the research of computed tomography technology. This paper d...With the development of the compressive sensing theory, the image reconstruction from the projections viewed in limited angles is one of the hot problems in the research of computed tomography technology. This paper develops an iterative algorithm for image reconstruction, which can fit the most cases. This method gives an image reconstruction flow with the difference image vector, which is based on the concept that the difference image vector between the reconstructed and the reference image is sparse enough. Then the l1-norm minimization method is used to reconstruct the difference vector to recover the image for flat subjects in limited angles. The algorithm has been tested with a thin planar phantom and a real object in limited-view projection data. Moreover, all the studies showed the satisfactory results in accuracy at a rather high reconstruction speed.展开更多
Coordinate descent method is a unconstrained optimization technique. When it is applied to support vector machine （SVM）, at each step the method updates one component of w by solving a one-variable sub-problem while...Coordinate descent method is a unconstrained optimization technique. When it is applied to support vector machine （SVM）, at each step the method updates one component of w by solving a one-variable sub-problem while fixing other components. All components of w update after one iteration. Then go to next iteration. Though the method converges and converges fast in the beginning, it converges slow for final convergence. To improve the speed of final convergence of coordinate descent method, Hooke and Jeeves algorithm which adds pattern search after every iteration in coordinate descent method was applied to SVM and a global Newton algorithm was used to solve one-variable subproblems. We proved the convergence of the algorithm. Experimental results show Hooke and Jeeves＇ method does accelerate convergence specially for final convergence and achieves higher testing accuracy more quickly in classification.展开更多
基金Supported by the State Foundations of Ph.D.Units(20020141013)Supported by the NSF of China(10001007)
文摘Some properties of a class of quasi-differentiable functions（the difference of two finite convex functions） are considered in this paper. And the convergence of the steepest descent algorithm for unconstrained and constrained quasi-differentiable programming is proved.
基金supported by the Fundamental Research Funds for the Central Universities(No.56XAA17075)
文摘A gradient descent algorithm with adjustable parameter for attitude estimation is developed,aiming at the attitude measurement for small unmanned aerial vehicle(UAV)in real-time flight conditions.The accelerometer and magnetometer are introduced to construct an error equation with the gyros,thus the drifting characteristics of gyroscope can be compensated by solving the error equation utilized by the gradient descent algorithm.Performance of the presented algorithm is evaluated using a self-proposed micro-electro-mechanical system(MEMS)based attitude heading reference system which is mounted on a tri-axis turntable.The on-ground,turntable and flight experiments indicate that the estimation attitude has a good accuracy.Also,the presented system is compared with an open-source flight control system which runs extended Kalman filter(EKF),and the results show that the attitude control system using the gradient descent method can estimate the attitudes for UAV effectively.
基金Supported by the National Science foundation of China(10671126, 40771095)the Key Project for Fundamental Research of STCSM(06JC14057)+1 种基金Shanghai Leading Academic Discipline Project(S30501)the Innovation Fund Project for Graduate Students of Shanghai(JWCXSL0801)
文摘Under some assumptions, the solution set of a nonlinear complementarity problem coincides with the set of local minima of the corresponding minimization problem. This paper uses a family of new merit functions to deal with nonlinear complementarity problem where the underlying function is assumed to be a continuous but not necessarily locally Lipschitzian map and gives a descent algorithm for solving the nonsmooth continuous complementarity problems. In addition, the global convergence of the derivative free descent algorithm is also proved.
基金Acknowledgment： This work was partly supported by the National Natural Science Foundation of China（60672150） and Science and Technology Planning Project of Shenzhen, China （szkj0706）.
基金supported by the National Natural Science Foundation of China(Grant Nos.12075159,12171044,and 12005015)Beijing Natural Science Foundation(Grant No.Z190005)Academy for Multidisciplinary Studies,Capital Normal University,Academician Innovation Platform of Hainan Province,and Shenzhen Institute for Quantum Science and Engineering,Southern University of Science and Technology(Grant No.SIQSE202001)。
文摘The gradient descent approach is the key ingredient in variational quantum algorithms and machine learning tasks,which is an optimization algorithm for finding a local minimum of an objective function.The quantum versions of gradient descent have been investigated and implemented in calculating molecular ground states and optimizing polynomial functions.Based on the quantum gradient descent algorithm and Choi-Jamiolkowski isomorphism,we present approaches to simulate efficiently the nonequilibrium steady states of Markovian open quantum many-body systems.Two strategies are developed to evaluate the expectation values of physical observables on the nonequilibrium steady states.Moreover,we adapt the quantum gradient descent algorithm to solve linear algebra problems including linear systems of equations and matrix-vector multiplications,by converting these algebraic problems into the simulations of closed quantum systems with well-defined Hamiltonians.Detailed examples are given to test numerically the effectiveness of the proposed algorithms for the dissipative quantum transverse Ising models and matrix-vector multiplications.
基金supported by the National Natural Science Foundation of China(No.12001144)Zhejiang Provincial Natural Science Foundation of China(No.LQ20A010007)NSF/DMS-2152961。
文摘In this paper,the authors propose a novel smoothing descent type algorithm with extrapolation for solving a class of constrained nonsmooth and nonconvex problems,where the nonconvex term is possibly nonsmooth.Their algorithm adopts the proximal gradient algorithm with extrapolation and a safe-guarding policy to minimize the smoothed objective function for better practical and theoretical performance.Moreover,the algorithm uses a easily checking rule to update the smoothing parameter to ensure that any accumulation point of the generated sequence is an(afne-scaled)Clarke stationary point of the original nonsmooth and nonconvex problem.Their experimental results indicate the effectiveness of the proposed algorithm.
基金supported by the National Natural Science Foundation of China (No.19731001) and theCroucher Foundation of Hong Kong
文摘In this paper, we give a descent algorithm for solving quadratic bilevel programming problems. It is proved that the descent algorithm finds a locally optimal solution to a quadratic bilevel programming problem in a finite number of iterations. Two numerical examples are given to illustrate this algorithm.
基金National Natural Science Foundation of China(62373187)Forward-looking Layout Special Projects(ILA220591A22)。
文摘In the field of calculating the attack area of air-to-air missiles in modern air combat scenarios,the limitations of existing research,including real-time calculation,accuracy efficiency trade-off,and the absence of the three-dimensional attack area model,restrict their practical applications.To address these issues,an improved backtracking algorithm is proposed to improve calculation efficiency.A significant reduction in solution time and maintenance of accuracy in the three-dimensional attack area are achieved by using the proposed algorithm.Furthermore,the age-layered population structure genetic programming(ALPS-GP)algorithm is introduced to determine an analytical polynomial model of the three-dimensional attack area,considering real-time requirements.The accuracy of the polynomial model is enhanced through the coefficient correction using an improved gradient descent algorithm.The study reveals a remarkable combination of high accuracy and efficient real-time computation,with a mean error of 91.89 m using the analytical polynomial model of the three-dimensional attack area solved in just 10^(-4)s,thus meeting the requirements of real-time combat scenarios.
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A large number of sparse signal reconstruction algorithms have been continuously proposed, but almost all greedy algorithms add a fixed number of indices to the support set in each iteration. Although the mechanism of selecting the fixed number of indexes improves the reconstruction efficiency, it also brings the problem of low index selection accuracy. Based on the full study of the theory of compressed sensing, we propose a dynamic indexes selection strategy based on residual update to improve the performance of the compressed sampling matching pursuit algorithm (CoSaMP). As an extension of CoSaMP algorithm, the proposed algorithm adopts a residual comparison strategy to improve the accuracy of backtracking selected indexes. This backtracking strategy can efficiently select backtracking indexes. And without increasing the computational complexity, the proposed improvement algorithm has a higher exact reconstruction rate and peak signal to noise ratio (PSNR). Simulation results demonstrate the proposed algorithm significantly outperforms the CoSaMP for image recovery and one-dimensional signal.
基金Project supported by the National Basic Research Program of China(Grant No.2006CB7057005)the National High Technology Research and Development Program of China(Grant No.2009AA012200)the National Natural Science Foundation of China (Grant No.60672104)
文摘With the development of the compressive sensing theory, the image reconstruction from the projections viewed in limited angles is one of the hot problems in the research of computed tomography technology. This paper develops an iterative algorithm for image reconstruction, which can fit the most cases. This method gives an image reconstruction flow with the difference image vector, which is based on the concept that the difference image vector between the reconstructed and the reference image is sparse enough. Then the l1-norm minimization method is used to reconstruct the difference vector to recover the image for flat subjects in limited angles. The algorithm has been tested with a thin planar phantom and a real object in limited-view projection data. Moreover, all the studies showed the satisfactory results in accuracy at a rather high reconstruction speed.
基金supported by the National Natural Science Foundation of China (6057407560705004)
文摘Coordinate descent method is a unconstrained optimization technique. When it is applied to support vector machine （SVM）, at each step the method updates one component of w by solving a one-variable sub-problem while fixing other components. All components of w update after one iteration. Then go to next iteration. Though the method converges and converges fast in the beginning, it converges slow for final convergence. To improve the speed of final convergence of coordinate descent method, Hooke and Jeeves algorithm which adds pattern search after every iteration in coordinate descent method was applied to SVM and a global Newton algorithm was used to solve one-variable subproblems. We proved the convergence of the algorithm. Experimental results show Hooke and Jeeves＇ method does accelerate convergence specially for final convergence and achieves higher testing accuracy more quickly in classification.
