The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on...The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on unconstrained smooth con-vex optimization problems.In this paper,on the basis of primal-dual dynamical approach,Nesterov accelerated dynamical approach,projection operator and directional gradient,we present two accelerated primal-dual projection neurodynamic approaches with time scaling to address convex optimization problems with smooth and nonsmooth objective functions subject to linear and set constraints,which consist of a second-order ODE(ordinary differential equation)or differential conclusion system for the primal variables and a first-order ODE for the dual vari-ables.By satisfying specific conditions for time scaling,we demonstrate that the proposed approaches have a faster conver-gence rate.This only requires assuming convexity of the objective function.We validate the effectiveness of our proposed two accel-erated primal-dual projection neurodynamic approaches through numerical experiments.展开更多
In this article, a general Lyapunov stability theory of nonlinear systems is put forward and it contains asymptotic/finite-time/fast finite-time/fixed-time stability. Especially, a more accurate estimate of the settli...In this article, a general Lyapunov stability theory of nonlinear systems is put forward and it contains asymptotic/finite-time/fast finite-time/fixed-time stability. Especially, a more accurate estimate of the settling-time function is exhibited for fixedtime stability, and it is still extraneous to the initial conditions.This can be applied to obtain less conservative convergence time of the practical systems without the information of the initial conditions. As an application, the given fixed-time stability theorem is used to resolve time-varying(TV) convex optimization problem.By the Newton's method, two classes of new dynamical systems are constructed to guarantee that the solution of the dynamic system can track to the optimal trajectory of the unconstrained and equality constrained TV convex optimization problems in fixed time, respectively. Without the exact knowledge of the time derivative of the cost function gradient, a fixed-time dynamical non-smooth system is established to overcome the issue of robust TV convex optimization. Two examples are provided to illustrate the effectiveness of the proposed TV convex optimization algorithms. Subsequently, the fixed-time stability theory is extended to the theories of predefined-time/practical predefined-time stability whose bound of convergence time can be arbitrarily given in advance, without tuning the system parameters. Under which, TV convex optimization problem is solved. The previous two examples are used to demonstrate the validity of the predefined-time TV convex optimization algorithms.展开更多
Detection of wood plate surface defects using image processing is a complicated problem in the forest industry as the image of the wood surface contains different kinds of defects. In order to obtain complete defect i...Detection of wood plate surface defects using image processing is a complicated problem in the forest industry as the image of the wood surface contains different kinds of defects. In order to obtain complete defect images, we used convex optimization(CO) with different weights as a pretreatment method for smoothing and the Otsu segmentation method to obtain the target defect area images. Structural similarity(SSIM) results between original image and defect image were calculated to evaluate the performance of segmentation with different convex optimization weights. The geometric and intensity features of defects were extracted before constructing a classification and regression tree(CART) classifier. The average accuracy of the classifier is 94.1% with four types of defects on Xylosma congestum wood plate surface: pinhole, crack,live knot and dead knot. Experimental results showed that CO can save the edge of target defects maximally, SSIM can select the appropriate weight for CO, and the CART classifier appears to have the advantages of good adaptability and high classification accuracy.展开更多
High-area/mass ratio landers driven by Solar Radiation Pressure(SRP)have potential applications for future asteroid landing missions.This paper develops a new convex optimization-based method for planning trajectories...High-area/mass ratio landers driven by Solar Radiation Pressure(SRP)have potential applications for future asteroid landing missions.This paper develops a new convex optimization-based method for planning trajectories driven by SRP.A Minimum Landing Error(MLE)control problem is formulated to enable planning SRP-controlled trajectories with different flight times.It is transformed into Second Order Cone Programming(SOCP)successfully by a series of different convexification technologies.A trust region constraint and a modified MLE objective function are used to guarantee the convergence performance of the optimization algorithm.Thereafter,the SRP-driven trajectory optimal control problem is converted equivalently into a sequence of convex optimal control problems that can be solved effectively.A set of numerical simulation results has verified the effectiveness and feasibility of the proposed optimization method.展开更多
A convex optimization model predicts an output from an input by solving a convex optimization problem.The class of convex optimization models is large,and includes as special cases many well-known models like linear a...A convex optimization model predicts an output from an input by solving a convex optimization problem.The class of convex optimization models is large,and includes as special cases many well-known models like linear and logistic regression.We propose a heuristic for learning the parameters in a convex optimization model given a dataset of input-output pairs,using recently developed methods for differentiating the solution of a convex optimization problem with respect to its parameters.We describe three general classes of convex optimization models,maximum a posteriori(MAP)models,utility maximization models,and agent models,and present a numerical experiment for each.展开更多
In this paper,an integrated guidance and control approach is presented to improve the performance of the missile interception.The approach includes damping augmented system with attitude rate feedback to decrease the ...In this paper,an integrated guidance and control approach is presented to improve the performance of the missile interception.The approach includes damping augmented system with attitude rate feedback to decrease the oscillation during the homing phase for missiles with low damping.In addition,physical constraints,which can affect the performance of the missile interception,such as acceleration limit,seeker’s look angle,and look angle rate constraints are considered.The integrated guidance and control problem is formulated as a convex quadratic optimization problem with equality and inequality constraints,and the solution is obtained by a primal–dual interior point method.The performance of the proposed method is verified through several numerical examples.展开更多
Massive multiple-input multiple-output(MIMO)technology enables higher data rate transmission in the future mobile communications.However,exploiting a large number of antenna elements at base station(BS)makes effective...Massive multiple-input multiple-output(MIMO)technology enables higher data rate transmission in the future mobile communications.However,exploiting a large number of antenna elements at base station(BS)makes effective implementation of massive MIMO challenging,due to the size and weight limits of the masssive MIMO that are located on each BS.Therefore,in order to miniaturize the massive MIMO,it is crucial to reduce the number of antenna elements via effective methods such as sparse array synthesis.In this paper,a multiple-pattern synthesis is considered towards convex optimization(CO).The joint convex optimization(JCO)based synthesis is proposed to construct a codebook for beamforming.Then,a criterion containing multiple constraints is developed,in which the sparse array is required to fullfill all constraints.Finally,extensive evaluations are performed under realistic simulation settings.The results show that with the same number of antenna elements,sparse array using the proposed JCO-based synthesis outperforms not only the uniform array,but also the sparse array with the existing CO-based synthesis method.Furthermore,with a half of the number of antenna elements that on the uniform array,the performance of the JCO-based sparse array approaches to that of the uniform array.展开更多
Control systems designed by the principle of matching gives rise to problems of evaluating the peak output. This paper proposes a practical method for computing the peak output of linear time-invariant and non-anticip...Control systems designed by the principle of matching gives rise to problems of evaluating the peak output. This paper proposes a practical method for computing the peak output of linear time-invariant and non-anticipative systems for a class of possible sets that are characterized with many bounding conditions on the two- and/or the infinity-norms of the inputs and their derivatives. The original infinite-dimensional convex optimization problem is approximated as a large-scale convex programme defined in a Euclidean space, which are associated with sparse matrices and thus can be solved efficiently in practice. The numerical results show that the method performs satisfactorily, and that using a possible set with many bounding conditions can help to reduce the design conservatism and thereby yield a better match.展开更多
In this paper, a primal-dual path-following interior-point algorithm for linearly constrained convex optimization(LCCO) is presented.The algorithm is based on a new technique for finding a class of search directions a...In this paper, a primal-dual path-following interior-point algorithm for linearly constrained convex optimization(LCCO) is presented.The algorithm is based on a new technique for finding a class of search directions and the strategy of the central path.At each iteration, only full-Newton steps are used.Finally, the favorable polynomial complexity bound for the algorithm with the small-update method is deserved, namely, O(√n log n /ε).展开更多
The stabilization problem of linear time-varying systems with both state and input constraints is considered. Sufficient conditions for the existence of the solution to this problem are derived and a gain-switched（ga...The stabilization problem of linear time-varying systems with both state and input constraints is considered. Sufficient conditions for the existence of the solution to this problem are derived and a gain-switched（gain-scheduled） state feedback control scheme is built to stabilize the constrained timevarying system. The design problem is transformed to a series of convex feasibility problems which can be solved efficiently. A design example is given to illustrate the effect of the proposed algorithm.展开更多
The service quality of a workstation depends mainly on its service load, ifnot taking into account all kinds of devices' break-downs. In this article, an optimization modelwith inequality constraints is proposed, ...The service quality of a workstation depends mainly on its service load, ifnot taking into account all kinds of devices' break-downs. In this article, an optimization modelwith inequality constraints is proposed, which aims to minimize the service load. A noveltransformation of optimization variables is also devised and the constraints are properly combinedso as to make this model into a convex one, whose corresponding Lagrange function and the KKTconditions are established afterwards. The interior-point method for convex optimization ispresented here as an efficient computation tool. Finally, this model is evaluated by a real example,from which conclusions are reached that the interior-point method possesses advantages such asfaster convergeoce and fewer iterations and it is possible to make complicated nonlinearoptimization problems exhibit convexity so as to obtain the optimum.展开更多
On the basis of the queuing theory, a nonlinear optimal load allocation model is proposed. A novel transformafion method for the optimization variables is also presented, and the constraints are properly combined so a...On the basis of the queuing theory, a nonlinear optimal load allocation model is proposed. A novel transformafion method for the optimization variables is also presented, and the constraints are properly combined so as to make this model convex. The interior-point method for convex optimization is presented as an efficient computational tool. Finally, this model is evaluated by a real example,from which the following conclusions are drawn： the optimum result can ensure the full utilization of machines and the smallest amount of WIP （work-in-progress） in queuing systems; the interior-point method needs a few iterations with significant computational savings; other performance measures of queuing systems can also be optimized in a similar way.展开更多
We present a novel algorithm that can determine rotation-related parameters of a target using FMCW （frequency modulated continuous wave） radars, not utilizing inertia information of the target. More specifically, th...We present a novel algorithm that can determine rotation-related parameters of a target using FMCW （frequency modulated continuous wave） radars, not utilizing inertia information of the target. More specifically, the proposed algorithm estimates the angular velocity vector of a target as a function of time, as well as the distances of scattering points in the wing tip from the rotation axis, just by analyzing Doppler spectrograms obtained from three or more radars. The obtained parameter values will be useful to classify targets such as hostile warheads or missiles for real-time operation, or to analyze the trajectory of targets under test for the instrumentation radar operation. The proposed algorithm is based on the convex optimization to obtain the rotation-related parameters. The performance of the proposed algorithm is assessed through Monte Carlo simulations. Estimation performance of the proposed algorithm depends on the target and radar geometry and improves as the number of iterations of the convex optimization steps increases.展开更多
In this paper, we report in-depth analysis and research on the optimizing computer network structure based on genetic algorithm and modified convex optimization theory. Machine learning method has been widely used in ...In this paper, we report in-depth analysis and research on the optimizing computer network structure based on genetic algorithm and modified convex optimization theory. Machine learning method has been widely used in the background and one of its core problems is to solve the optimization problem. Unlike traditional batch algorithm, stochastic gradient descent algorithm in each iteration calculation, the optimization of a single sample point only losses could greatly reduce the memory overhead. The experiment illustrates the feasibility of our proposed approach.展开更多
In this paper, we present a regularized Newton method (M-RNM) with correction for minimizing a convex function whose Hessian matrices may be singular. At every iteration, not only a RNM step is computed but also two c...In this paper, we present a regularized Newton method (M-RNM) with correction for minimizing a convex function whose Hessian matrices may be singular. At every iteration, not only a RNM step is computed but also two correction steps are computed. We show that if the objective function is LC<sup>2</sup>, then the method posses globally convergent. Numerical results show that the new algorithm performs very well.展开更多
The traditional guidance law only guarantees the accuracy of attacking a target. However, the look angle and acceleration constraints are indispensable in applications. A new adaptive three-dimensional proportional na...The traditional guidance law only guarantees the accuracy of attacking a target. However, the look angle and acceleration constraints are indispensable in applications. A new adaptive three-dimensional proportional navigation(PN) guidance law is proposed based on convex optimization. Decomposition of the three-dimensional space is carried out to establish threedimensional kinematic engagements. The constraints and the performance index are disposed by using the convex optimization method. PN guidance gains can be obtained by solving the optimization problem. This solution is more rapid and programmatic than the traditional method and provides a foundation for future online guidance methods, which is of great value for engineering applications.展开更多
In this paper,we consider online convex optimization(OCO)with time-varying loss and constraint functions.Specifically,the decision-maker chooses sequential decisions based only on past information;meantime,the loss an...In this paper,we consider online convex optimization(OCO)with time-varying loss and constraint functions.Specifically,the decision-maker chooses sequential decisions based only on past information;meantime,the loss and constraint functions are revealed over time.We first develop a class of model-based augmented Lagrangian methods(MALM)for time-varying functional constrained OCO(without feedback delay).Under standard assumptions,we establish sublinear regret and sublinear constraint violation of MALM.Furthermore,we extend MALM to deal with time-varying functional constrained OCO with delayed feedback,in which the feedback information of loss and constraint functions is revealed to decision-maker with delays.Without additional assumptions,we also establish sublinear regret and sublinear constraint violation for the delayed version of MALM.Finally,numerical results for several examples of constrained OCO including online network resource allocation,online logistic regression and online quadratically constrained quadratical program are presented to demonstrate the efficiency of the proposed algorithms.展开更多
A neurodynamic method(NdM)for convex optimization is proposed in this paper with an equality constraint.The method utilizes a neurodynamic system(NdS)that converges to the optimal solution of a convex optimization pro...A neurodynamic method(NdM)for convex optimization is proposed in this paper with an equality constraint.The method utilizes a neurodynamic system(NdS)that converges to the optimal solution of a convex optimization problem in a fixed time.Due to its mathematical simplicity,it can also be combined with reinforcement learning(RL)to solve a class of nonconvex optimization problems.To maintain the mathematical simplicity of NdS,zero-sum initial constraints are introduced to reduce the number of auxiliary multipliers.First,the initial sum of the state variables must satisfy the equality constraint.Second,the sum of their derivatives is designed to remain zero.In order to apply the proposed convex optimization algorithm to nonconvex optimization with mixed constraints,the virtual actions in RL are redefined to avoid the use of NdS inequality constrained multipliers.The proposed NdM plays an effective search tool in constrained nonconvex optimization algorithms.Numerical examples demonstrate the effectiveness of the proposed algorithm.展开更多
In this paper,we investigate the application of the Unmanned Aerial Vehicle(UAV)-enabled relaying system in emergency communications,where one UAV is applied as a relay to help transmit information from ground users t...In this paper,we investigate the application of the Unmanned Aerial Vehicle(UAV)-enabled relaying system in emergency communications,where one UAV is applied as a relay to help transmit information from ground users to a Base Station(BS).We maximize the total transmitted data from the users to the BS,by optimizing the user communication scheduling and association along with the power allocation and the trajectory of the UAV.To solve this non-convex optimization problem,we propose the traditional Convex Optimization(CO)and the Reinforcement Learning(RL)-based approaches.Specifically,we apply the block coordinate descent and successive convex approximation techniques in the CO approach,while applying the soft actor-critic algorithm in the RL approach.The simulation results show that both approaches can solve the proposed optimization problem and obtain good results.Moreover,the RL approach establishes emergency communications more rapidly than the CO approach once the training process has been completed.展开更多
In this paper,we develop an inexact symmetric proximal alternating direction method of multipliers(ISPADMM)with two convex combinations(ISPADMM-tcc)for solving two-block separable convex optimization problems with lin...In this paper,we develop an inexact symmetric proximal alternating direction method of multipliers(ISPADMM)with two convex combinations(ISPADMM-tcc)for solving two-block separable convex optimization problems with linear equality constraints.Specifically,the convex combination technique is incorporated into the proximal centers of both subproblems.We then approximately solve these two subproblems based on relative error criteria.The global convergence,and O(1/N)ergodic sublinear convergence rate measured by the function value residual and constraint violation are established under some mild conditions,where N denotes the number of iterations.Finally,numerical experiments on solving the l1-regularized analysis sparse recovery and the elastic net regularization regression problems illustrate the feasibility and effectiveness of the proposed method.展开更多
基金supported by the National Natural Science Foundation of China(62176218,62176027)the Fundamental Research Funds for the Central Universities(XDJK2020TY003)the Funds for Chongqing Talent Plan(cstc2024ycjh-bgzxm0082)。
文摘The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on unconstrained smooth con-vex optimization problems.In this paper,on the basis of primal-dual dynamical approach,Nesterov accelerated dynamical approach,projection operator and directional gradient,we present two accelerated primal-dual projection neurodynamic approaches with time scaling to address convex optimization problems with smooth and nonsmooth objective functions subject to linear and set constraints,which consist of a second-order ODE(ordinary differential equation)or differential conclusion system for the primal variables and a first-order ODE for the dual vari-ables.By satisfying specific conditions for time scaling,we demonstrate that the proposed approaches have a faster conver-gence rate.This only requires assuming convexity of the objective function.We validate the effectiveness of our proposed two accel-erated primal-dual projection neurodynamic approaches through numerical experiments.
基金supported in part by the National Natural Science Foundation of China(62203281)。
文摘In this article, a general Lyapunov stability theory of nonlinear systems is put forward and it contains asymptotic/finite-time/fast finite-time/fixed-time stability. Especially, a more accurate estimate of the settling-time function is exhibited for fixedtime stability, and it is still extraneous to the initial conditions.This can be applied to obtain less conservative convergence time of the practical systems without the information of the initial conditions. As an application, the given fixed-time stability theorem is used to resolve time-varying(TV) convex optimization problem.By the Newton's method, two classes of new dynamical systems are constructed to guarantee that the solution of the dynamic system can track to the optimal trajectory of the unconstrained and equality constrained TV convex optimization problems in fixed time, respectively. Without the exact knowledge of the time derivative of the cost function gradient, a fixed-time dynamical non-smooth system is established to overcome the issue of robust TV convex optimization. Two examples are provided to illustrate the effectiveness of the proposed TV convex optimization algorithms. Subsequently, the fixed-time stability theory is extended to the theories of predefined-time/practical predefined-time stability whose bound of convergence time can be arbitrarily given in advance, without tuning the system parameters. Under which, TV convex optimization problem is solved. The previous two examples are used to demonstrate the validity of the predefined-time TV convex optimization algorithms.
基金supported by the Fund of Forestry 948project(2015-4-52)the Fundamental Research Funds for the Central Universities(2572017DB05)the Natural Science Foundation of Heilongjiang Province(C2017005)
文摘Detection of wood plate surface defects using image processing is a complicated problem in the forest industry as the image of the wood surface contains different kinds of defects. In order to obtain complete defect images, we used convex optimization(CO) with different weights as a pretreatment method for smoothing and the Otsu segmentation method to obtain the target defect area images. Structural similarity(SSIM) results between original image and defect image were calculated to evaluate the performance of segmentation with different convex optimization weights. The geometric and intensity features of defects were extracted before constructing a classification and regression tree(CART) classifier. The average accuracy of the classifier is 94.1% with four types of defects on Xylosma congestum wood plate surface: pinhole, crack,live knot and dead knot. Experimental results showed that CO can save the edge of target defects maximally, SSIM can select the appropriate weight for CO, and the CART classifier appears to have the advantages of good adaptability and high classification accuracy.
基金supported by the National Natural Science Foundation of China(No.12102177)the Natural Science Foundation of Jiangsu Province,China(No.BK20180410)+2 种基金the Young Elite Scientists Sponsorship Program by CAST,China(No.2018QNRC001)the Open Project Program of Tianjin Key Laboratory of Microgravity and Hypogravity Environment Simulation Technology,China(No.WDZL2020-07)the Foundation of Graduate Innovation Center at NUAA,China(No.kfjj20201503).
文摘High-area/mass ratio landers driven by Solar Radiation Pressure(SRP)have potential applications for future asteroid landing missions.This paper develops a new convex optimization-based method for planning trajectories driven by SRP.A Minimum Landing Error(MLE)control problem is formulated to enable planning SRP-controlled trajectories with different flight times.It is transformed into Second Order Cone Programming(SOCP)successfully by a series of different convexification technologies.A trust region constraint and a modified MLE objective function are used to guarantee the convergence performance of the optimization algorithm.Thereafter,the SRP-driven trajectory optimal control problem is converted equivalently into a sequence of convex optimal control problems that can be solved effectively.A set of numerical simulation results has verified the effectiveness and feasibility of the proposed optimization method.
文摘A convex optimization model predicts an output from an input by solving a convex optimization problem.The class of convex optimization models is large,and includes as special cases many well-known models like linear and logistic regression.We propose a heuristic for learning the parameters in a convex optimization model given a dataset of input-output pairs,using recently developed methods for differentiating the solution of a convex optimization problem with respect to its parameters.We describe three general classes of convex optimization models,maximum a posteriori(MAP)models,utility maximization models,and agent models,and present a numerical experiment for each.
文摘In this paper,an integrated guidance and control approach is presented to improve the performance of the missile interception.The approach includes damping augmented system with attitude rate feedback to decrease the oscillation during the homing phase for missiles with low damping.In addition,physical constraints,which can affect the performance of the missile interception,such as acceleration limit,seeker’s look angle,and look angle rate constraints are considered.The integrated guidance and control problem is formulated as a convex quadratic optimization problem with equality and inequality constraints,and the solution is obtained by a primal–dual interior point method.The performance of the proposed method is verified through several numerical examples.
文摘Massive multiple-input multiple-output(MIMO)technology enables higher data rate transmission in the future mobile communications.However,exploiting a large number of antenna elements at base station(BS)makes effective implementation of massive MIMO challenging,due to the size and weight limits of the masssive MIMO that are located on each BS.Therefore,in order to miniaturize the massive MIMO,it is crucial to reduce the number of antenna elements via effective methods such as sparse array synthesis.In this paper,a multiple-pattern synthesis is considered towards convex optimization(CO).The joint convex optimization(JCO)based synthesis is proposed to construct a codebook for beamforming.Then,a criterion containing multiple constraints is developed,in which the sparse array is required to fullfill all constraints.Finally,extensive evaluations are performed under realistic simulation settings.The results show that with the same number of antenna elements,sparse array using the proposed JCO-based synthesis outperforms not only the uniform array,but also the sparse array with the existing CO-based synthesis method.Furthermore,with a half of the number of antenna elements that on the uniform array,the performance of the JCO-based sparse array approaches to that of the uniform array.
文摘Control systems designed by the principle of matching gives rise to problems of evaluating the peak output. This paper proposes a practical method for computing the peak output of linear time-invariant and non-anticipative systems for a class of possible sets that are characterized with many bounding conditions on the two- and/or the infinity-norms of the inputs and their derivatives. The original infinite-dimensional convex optimization problem is approximated as a large-scale convex programme defined in a Euclidean space, which are associated with sparse matrices and thus can be solved efficiently in practice. The numerical results show that the method performs satisfactorily, and that using a possible set with many bounding conditions can help to reduce the design conservatism and thereby yield a better match.
基金supported by the Shanghai Pujiang Program (Grant No.06PJ14039)the Science Foundation of Shanghai Municipal Commission of Education (Grant No.06NS031)
文摘In this paper, a primal-dual path-following interior-point algorithm for linearly constrained convex optimization(LCCO) is presented.The algorithm is based on a new technique for finding a class of search directions and the strategy of the central path.At each iteration, only full-Newton steps are used.Finally, the favorable polynomial complexity bound for the algorithm with the small-update method is deserved, namely, O(√n log n /ε).
基金supported by the National Natural Science Foundation of China(6132106261503100)the China Postdoctoral Science Foundation(2014M550189)
文摘The stabilization problem of linear time-varying systems with both state and input constraints is considered. Sufficient conditions for the existence of the solution to this problem are derived and a gain-switched（gain-scheduled） state feedback control scheme is built to stabilize the constrained timevarying system. The design problem is transformed to a series of convex feasibility problems which can be solved efficiently. A design example is given to illustrate the effect of the proposed algorithm.
文摘The service quality of a workstation depends mainly on its service load, ifnot taking into account all kinds of devices' break-downs. In this article, an optimization modelwith inequality constraints is proposed, which aims to minimize the service load. A noveltransformation of optimization variables is also devised and the constraints are properly combinedso as to make this model into a convex one, whose corresponding Lagrange function and the KKTconditions are established afterwards. The interior-point method for convex optimization ispresented here as an efficient computation tool. Finally, this model is evaluated by a real example,from which conclusions are reached that the interior-point method possesses advantages such asfaster convergeoce and fewer iterations and it is possible to make complicated nonlinearoptimization problems exhibit convexity so as to obtain the optimum.
文摘On the basis of the queuing theory, a nonlinear optimal load allocation model is proposed. A novel transformafion method for the optimization variables is also presented, and the constraints are properly combined so as to make this model convex. The interior-point method for convex optimization is presented as an efficient computational tool. Finally, this model is evaluated by a real example,from which the following conclusions are drawn： the optimum result can ensure the full utilization of machines and the smallest amount of WIP （work-in-progress） in queuing systems; the interior-point method needs a few iterations with significant computational savings; other performance measures of queuing systems can also be optimized in a similar way.
文摘We present a novel algorithm that can determine rotation-related parameters of a target using FMCW （frequency modulated continuous wave） radars, not utilizing inertia information of the target. More specifically, the proposed algorithm estimates the angular velocity vector of a target as a function of time, as well as the distances of scattering points in the wing tip from the rotation axis, just by analyzing Doppler spectrograms obtained from three or more radars. The obtained parameter values will be useful to classify targets such as hostile warheads or missiles for real-time operation, or to analyze the trajectory of targets under test for the instrumentation radar operation. The proposed algorithm is based on the convex optimization to obtain the rotation-related parameters. The performance of the proposed algorithm is assessed through Monte Carlo simulations. Estimation performance of the proposed algorithm depends on the target and radar geometry and improves as the number of iterations of the convex optimization steps increases.
文摘In this paper, we report in-depth analysis and research on the optimizing computer network structure based on genetic algorithm and modified convex optimization theory. Machine learning method has been widely used in the background and one of its core problems is to solve the optimization problem. Unlike traditional batch algorithm, stochastic gradient descent algorithm in each iteration calculation, the optimization of a single sample point only losses could greatly reduce the memory overhead. The experiment illustrates the feasibility of our proposed approach.
文摘In this paper, we present a regularized Newton method (M-RNM) with correction for minimizing a convex function whose Hessian matrices may be singular. At every iteration, not only a RNM step is computed but also two correction steps are computed. We show that if the objective function is LC<sup>2</sup>, then the method posses globally convergent. Numerical results show that the new algorithm performs very well.
基金supported by the National Natural Science Foundation of China(61803357)。
文摘The traditional guidance law only guarantees the accuracy of attacking a target. However, the look angle and acceleration constraints are indispensable in applications. A new adaptive three-dimensional proportional navigation(PN) guidance law is proposed based on convex optimization. Decomposition of the three-dimensional space is carried out to establish threedimensional kinematic engagements. The constraints and the performance index are disposed by using the convex optimization method. PN guidance gains can be obtained by solving the optimization problem. This solution is more rapid and programmatic than the traditional method and provides a foundation for future online guidance methods, which is of great value for engineering applications.
基金supported in part by the National Key R&D Program of China(No.2022YFA1004000)the National Natural Science Foundation of China(Nos.11971089 and 12271076).
文摘In this paper,we consider online convex optimization(OCO)with time-varying loss and constraint functions.Specifically,the decision-maker chooses sequential decisions based only on past information;meantime,the loss and constraint functions are revealed over time.We first develop a class of model-based augmented Lagrangian methods(MALM)for time-varying functional constrained OCO(without feedback delay).Under standard assumptions,we establish sublinear regret and sublinear constraint violation of MALM.Furthermore,we extend MALM to deal with time-varying functional constrained OCO with delayed feedback,in which the feedback information of loss and constraint functions is revealed to decision-maker with delays.Without additional assumptions,we also establish sublinear regret and sublinear constraint violation for the delayed version of MALM.Finally,numerical results for several examples of constrained OCO including online network resource allocation,online logistic regression and online quadratically constrained quadratical program are presented to demonstrate the efficiency of the proposed algorithms.
基金supported by the National Natural Science Foundation of China(Nos.61973070 and 62373089)the Nature Science Foundation of Liaoning Province,China(No.2022JH25/10100008)the SAPI Fundamental Research Funds,China(No.2018ZCX22).
文摘A neurodynamic method(NdM)for convex optimization is proposed in this paper with an equality constraint.The method utilizes a neurodynamic system(NdS)that converges to the optimal solution of a convex optimization problem in a fixed time.Due to its mathematical simplicity,it can also be combined with reinforcement learning(RL)to solve a class of nonconvex optimization problems.To maintain the mathematical simplicity of NdS,zero-sum initial constraints are introduced to reduce the number of auxiliary multipliers.First,the initial sum of the state variables must satisfy the equality constraint.Second,the sum of their derivatives is designed to remain zero.In order to apply the proposed convex optimization algorithm to nonconvex optimization with mixed constraints,the virtual actions in RL are redefined to avoid the use of NdS inequality constrained multipliers.The proposed NdM plays an effective search tool in constrained nonconvex optimization algorithms.Numerical examples demonstrate the effectiveness of the proposed algorithm.
基金supported in part by the Shenzhen Basic Research Project under Grant JCYJ20220531103008018 and Grant 20200812112423002in part by the Guangdong Basic Research Program under Grant 2019A1515110358,2021A1515012097in part by the open research fund of National Mobile Communications Research Laboratory,Southeast University (No.2021D16)。
文摘In this paper,we investigate the application of the Unmanned Aerial Vehicle(UAV)-enabled relaying system in emergency communications,where one UAV is applied as a relay to help transmit information from ground users to a Base Station(BS).We maximize the total transmitted data from the users to the BS,by optimizing the user communication scheduling and association along with the power allocation and the trajectory of the UAV.To solve this non-convex optimization problem,we propose the traditional Convex Optimization(CO)and the Reinforcement Learning(RL)-based approaches.Specifically,we apply the block coordinate descent and successive convex approximation techniques in the CO approach,while applying the soft actor-critic algorithm in the RL approach.The simulation results show that both approaches can solve the proposed optimization problem and obtain good results.Moreover,the RL approach establishes emergency communications more rapidly than the CO approach once the training process has been completed.
基金supported by the National Natural Science Foundation of China(12171106)the Guangxi Science and Technology Program(AD23023001)+4 种基金the Natural Science Foundation of Guangxi Province(2023GXNSFBA026029)the National Natural Science Foundation of China(12401403,12361063)the Research Project of Guangxi Minzu University(2022KJQD03)the Middle-aged and Young Teachers’Basic Ability Promotion Project of Guangxi Province(2023KY0168)the Xiangsihu Young Scholars Innovative Research Team of Guangxi Minzu University(2022GXUNXSHQN04).
文摘In this paper,we develop an inexact symmetric proximal alternating direction method of multipliers(ISPADMM)with two convex combinations(ISPADMM-tcc)for solving two-block separable convex optimization problems with linear equality constraints.Specifically,the convex combination technique is incorporated into the proximal centers of both subproblems.We then approximately solve these two subproblems based on relative error criteria.The global convergence,and O(1/N)ergodic sublinear convergence rate measured by the function value residual and constraint violation are established under some mild conditions,where N denotes the number of iterations.Finally,numerical experiments on solving the l1-regularized analysis sparse recovery and the elastic net regularization regression problems illustrate the feasibility and effectiveness of the proposed method.
