Improving numerical forecasting skill in the atmospheric and oceanic sciences by solving optimization problems is an important issue. One such method is to compute the conditional nonlinear optimal perturbation(CNOP),...Improving numerical forecasting skill in the atmospheric and oceanic sciences by solving optimization problems is an important issue. One such method is to compute the conditional nonlinear optimal perturbation(CNOP), which has been applied widely in predictability studies. In this study, the Differential Evolution(DE) algorithm, which is a derivative-free algorithm and has been applied to obtain CNOPs for exploring the uncertainty of terrestrial ecosystem processes, was employed to obtain the CNOPs for finite-dimensional optimization problems with ball constraint conditions using Burgers' equation. The aim was first to test if the CNOP calculated by the DE algorithm is similar to that computed by traditional optimization algorithms, such as the Spectral Projected Gradient(SPG2) algorithm. The second motive was to supply a possible route through which the CNOP approach can be applied in predictability studies in the atmospheric and oceanic sciences without obtaining a model adjoint system, or for optimization problems with non-differentiable cost functions. A projection skill was first explanted to the DE algorithm to calculate the CNOPs. To validate the algorithm, the SPG2 algorithm was also applied to obtain the CNOPs for the same optimization problems. The results showed that the CNOPs obtained by the DE algorithm were nearly the same as those obtained by the SPG2 algorithm in terms of their spatial distributions and nonlinear evolutions. The implication is that the DE algorithm could be employed to calculate the optimal values of optimization problems, especially for non-differentiable and nonlinear optimization problems associated with the atmospheric and oceanic sciences.展开更多
This paper develops a new algorithm based on the Projected Gradient Algorithm (PGA) for the design of FIR digital filters with "sum of power of two" coefficients. It is shown that the integer programming inv...This paper develops a new algorithm based on the Projected Gradient Algorithm (PGA) for the design of FIR digital filters with "sum of power of two" coefficients. It is shown that the integer programming involved in the FIR filter design can be solved by this algorithm. It is compared with the reported method for a SemiDefinite Programming (SDP) relaxation- based design. The simulations demonstrate that the new algorithm often yields the similar error performances of the FIR filter design, but the average CPU time of this approach is significantly reduced.展开更多
A real-time electronic image stabilization motion estimation method based on fast sub- block gray projection algorithm is proposed. In the method, each image is divided into a number of sub-blocks, and sub-blocks are ...A real-time electronic image stabilization motion estimation method based on fast sub- block gray projection algorithm is proposed. In the method, each image is divided into a number of sub-blocks, and sub-blocks are sifted with their gray gradients. After removing sub-blocks whose gray gradients are lower than the given threshold, the calculation amount of projection is reduced and the motion estimation accuracy is improved. Then gray projection is done in each remained sub- block, and global motion vector of the image is calculated according to the local motion vectors of sub-blocks and the affine motion model. The drawbacks as the local motions reducing the global mo- tion estimation accuracy and traditional gray projection algorithm could not deal with rotation are re- solved well by this algorithm. The experiment results show that the algorithm is more accurate and efficient than the gray projection algorithm.展开更多
Although many effective algorithms of the gradient projection type have been given, there exist some problems which are not solved in these algorithms. In this paper, we consider the problem with nonlinear equality an...Although many effective algorithms of the gradient projection type have been given, there exist some problems which are not solved in these algorithms. In this paper, we consider the problem with nonlinear equality and inequality constraints and have given a generalized gradient projection algorithm. The global convergence of the algorithm has been proved and the problems have been solved completely by our algorithm.展开更多
方位超分辨一直是雷达领域里受到广泛关注的研究课题,针对求解过程中遇到的病态性,深入研究了L1范数正则化方法及其约束方法。在目标稀疏性质的前提下,建立了L1范数正则化与约束L1范数正则化模型。鉴于雷达数据的维数较多,利用梯度投影...方位超分辨一直是雷达领域里受到广泛关注的研究课题,针对求解过程中遇到的病态性,深入研究了L1范数正则化方法及其约束方法。在目标稀疏性质的前提下,建立了L1范数正则化与约束L1范数正则化模型。鉴于雷达数据的维数较多,利用梯度投影算法对模型进行求解。在不同信噪比情况下对两个等幅点目标进行了计算机仿真,结果初步表明:随着信噪比的降低,两种算法的分辨效果变差,在相同条件下约束L1范数正则化方法分辨效果更好,在信噪比为0 d B时,仍可分辨相隔1/2半功率波束宽度的两个等幅点目标;同时约束L1范数正则化方法分辨性能优于L1范数正则化方法、迭代反卷积法、维纳逆滤波法和Richardson-Lucy算法(RL算法);此两种范数正则化方法具有较强的噪声适应能力,可用于雷达方位超分辨。展开更多
基金provided by grants from the LASG State Key Laboratory Special Fundthe National Natural Science Foundation of China (Grant Nos. 40905050, 40830955, and 41375111)
文摘Improving numerical forecasting skill in the atmospheric and oceanic sciences by solving optimization problems is an important issue. One such method is to compute the conditional nonlinear optimal perturbation(CNOP), which has been applied widely in predictability studies. In this study, the Differential Evolution(DE) algorithm, which is a derivative-free algorithm and has been applied to obtain CNOPs for exploring the uncertainty of terrestrial ecosystem processes, was employed to obtain the CNOPs for finite-dimensional optimization problems with ball constraint conditions using Burgers' equation. The aim was first to test if the CNOP calculated by the DE algorithm is similar to that computed by traditional optimization algorithms, such as the Spectral Projected Gradient(SPG2) algorithm. The second motive was to supply a possible route through which the CNOP approach can be applied in predictability studies in the atmospheric and oceanic sciences without obtaining a model adjoint system, or for optimization problems with non-differentiable cost functions. A projection skill was first explanted to the DE algorithm to calculate the CNOPs. To validate the algorithm, the SPG2 algorithm was also applied to obtain the CNOPs for the same optimization problems. The results showed that the CNOPs obtained by the DE algorithm were nearly the same as those obtained by the SPG2 algorithm in terms of their spatial distributions and nonlinear evolutions. The implication is that the DE algorithm could be employed to calculate the optimal values of optimization problems, especially for non-differentiable and nonlinear optimization problems associated with the atmospheric and oceanic sciences.
基金Supported by Shaanxi Province Natural Science Funds.
文摘This paper develops a new algorithm based on the Projected Gradient Algorithm (PGA) for the design of FIR digital filters with "sum of power of two" coefficients. It is shown that the integer programming involved in the FIR filter design can be solved by this algorithm. It is compared with the reported method for a SemiDefinite Programming (SDP) relaxation- based design. The simulations demonstrate that the new algorithm often yields the similar error performances of the FIR filter design, but the average CPU time of this approach is significantly reduced.
基金Supported by the National Defense Scientific Research Project （ B2220132013 ）
文摘A real-time electronic image stabilization motion estimation method based on fast sub- block gray projection algorithm is proposed. In the method, each image is divided into a number of sub-blocks, and sub-blocks are sifted with their gray gradients. After removing sub-blocks whose gray gradients are lower than the given threshold, the calculation amount of projection is reduced and the motion estimation accuracy is improved. Then gray projection is done in each remained sub- block, and global motion vector of the image is calculated according to the local motion vectors of sub-blocks and the affine motion model. The drawbacks as the local motions reducing the global mo- tion estimation accuracy and traditional gray projection algorithm could not deal with rotation are re- solved well by this algorithm. The experiment results show that the algorithm is more accurate and efficient than the gray projection algorithm.
基金the National Natural Science Foundation of China
文摘Although many effective algorithms of the gradient projection type have been given, there exist some problems which are not solved in these algorithms. In this paper, we consider the problem with nonlinear equality and inequality constraints and have given a generalized gradient projection algorithm. The global convergence of the algorithm has been proved and the problems have been solved completely by our algorithm.
文摘方位超分辨一直是雷达领域里受到广泛关注的研究课题,针对求解过程中遇到的病态性,深入研究了L1范数正则化方法及其约束方法。在目标稀疏性质的前提下,建立了L1范数正则化与约束L1范数正则化模型。鉴于雷达数据的维数较多,利用梯度投影算法对模型进行求解。在不同信噪比情况下对两个等幅点目标进行了计算机仿真,结果初步表明:随着信噪比的降低,两种算法的分辨效果变差,在相同条件下约束L1范数正则化方法分辨效果更好,在信噪比为0 d B时,仍可分辨相隔1/2半功率波束宽度的两个等幅点目标;同时约束L1范数正则化方法分辨性能优于L1范数正则化方法、迭代反卷积法、维纳逆滤波法和Richardson-Lucy算法(RL算法);此两种范数正则化方法具有较强的噪声适应能力,可用于雷达方位超分辨。
