A perturbation method is applied to study the structure of the ground state of the adiabatic quantum optimization for the exact cover 3 problem. It is found that the instantaneous ground state near the end of the evol...A perturbation method is applied to study the structure of the ground state of the adiabatic quantum optimization for the exact cover 3 problem. It is found that the instantaneous ground state near the end of the evolution is mainly composed of the eigenstates of the problem Hamiltonian, which are Hamming close to the solution state. And the instantaneous ground state immediately after the starting is mainly formed of low energy eigenstates of the problem Hamiltonian. These results are then applied to estimate the minimum gap for a special case.展开更多
The conditional nonlinear optimal perturbation （CNOP）, which is a nonlinear generalization of the linear singular vector （LSV）, is applied in important problems of atmospheric and oceanic sciences, including ENSO ...The conditional nonlinear optimal perturbation （CNOP）, which is a nonlinear generalization of the linear singular vector （LSV）, is applied in important problems of atmospheric and oceanic sciences, including ENSO predictability, targeted observations, and ensemble forecast. In this study, we investigate the computational cost of obtaining the CNOP by several methods. Differences and similarities, in terms of the computational error and cost in obtaining the CNOP, are compared among the sequential quadratic programming （SQP） algorithm, the limited memory Broyden-Fletcher-Goldfarb-Shanno （L-BFGS） algorithm, and the spectral projected gradients （SPG2） algorithm. A theoretical grassland ecosystem model and the classical Lorenz model are used as examples. Numerical results demonstrate that the computational error is acceptable with all three algorithms. The computational cost to obtain the CNOP is reduced by using the SQP algorithm. The experimental results also reveal that the L-BFGS algorithm is the most effective algorithm among the three optimization algorithms for obtaining the CNOP. The numerical results suggest a new approach and algorithm for obtaining the CNOP for a large-scale optimization problem.展开更多
In this paper, Homotopy perturbation method is used to find the approximate solution of the optimal control of linear systems. In this method the initial approximations are freely chosen, and a Homotopy is constructed...In this paper, Homotopy perturbation method is used to find the approximate solution of the optimal control of linear systems. In this method the initial approximations are freely chosen, and a Homotopy is constructed with an embedding parameter , which is considered as a “small parameter”. Some examples are given in order to find the approximate solution and verify the efficiency of the proposed method.展开更多
The existence of step-like contrast structure for a class of singularly perturbed optimal control problem is presented by contrast structure theory. By means of direct scheme of boundary function method, we construct ...The existence of step-like contrast structure for a class of singularly perturbed optimal control problem is presented by contrast structure theory. By means of direct scheme of boundary function method, we construct the uniformly valid asymptotic solution for the singularly perturbed optimal control problem. As an application, an example is given to illustrate the main result in this paper.展开更多
In this paper we establish a high order finite volume method for the fourth order singular perturbation problems.In conjunction with the optimal meshes,the numerical solutions resulting from the method have optimal co...In this paper we establish a high order finite volume method for the fourth order singular perturbation problems.In conjunction with the optimal meshes,the numerical solutions resulting from the method have optimal convergence order.Numerical experiments are presented to verify our theoretical estimates.展开更多
借助庞特里亚金最大值原理(Pontryagin′s Maximal Principle,PMP),将月球燃耗最优软着陆问题转化为终端时间自由型两点边值问题(Two Point Boundary Value Problem,TPBVP)。采用一种基于初值猜测技术的线性摄动法求解TPBVP,得到最优软...借助庞特里亚金最大值原理(Pontryagin′s Maximal Principle,PMP),将月球燃耗最优软着陆问题转化为终端时间自由型两点边值问题(Two Point Boundary Value Problem,TPBVP)。采用一种基于初值猜测技术的线性摄动法求解TPBVP,得到最优软着陆轨迹。仿真结果表明,初值猜测技术得出的伴随变量初值均落在线性摄动法的收敛区间内,收敛速度快,优化精度高。最后研究了不同制动推力大小对软着陆性能的影响,结论为:增大制动发动机推力,既可缩短软着陆的时间,又能减少软着陆的燃料消耗。展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.61173050)
文摘A perturbation method is applied to study the structure of the ground state of the adiabatic quantum optimization for the exact cover 3 problem. It is found that the instantaneous ground state near the end of the evolution is mainly composed of the eigenstates of the problem Hamiltonian, which are Hamming close to the solution state. And the instantaneous ground state immediately after the starting is mainly formed of low energy eigenstates of the problem Hamiltonian. These results are then applied to estimate the minimum gap for a special case.
基金provided by grants from National Natural Science Foundation of China (Nos.40905050,40805020,40830955)the state Key Development Program for Basic Research (Grant No.2006CB400503)the KZCX3-SW-230 of the Chinese Academy of Sciences (CAS),LASG Free Exploration Fund,and LASG State Key Laboratory Special Fund
文摘The conditional nonlinear optimal perturbation （CNOP）, which is a nonlinear generalization of the linear singular vector （LSV）, is applied in important problems of atmospheric and oceanic sciences, including ENSO predictability, targeted observations, and ensemble forecast. In this study, we investigate the computational cost of obtaining the CNOP by several methods. Differences and similarities, in terms of the computational error and cost in obtaining the CNOP, are compared among the sequential quadratic programming （SQP） algorithm, the limited memory Broyden-Fletcher-Goldfarb-Shanno （L-BFGS） algorithm, and the spectral projected gradients （SPG2） algorithm. A theoretical grassland ecosystem model and the classical Lorenz model are used as examples. Numerical results demonstrate that the computational error is acceptable with all three algorithms. The computational cost to obtain the CNOP is reduced by using the SQP algorithm. The experimental results also reveal that the L-BFGS algorithm is the most effective algorithm among the three optimization algorithms for obtaining the CNOP. The numerical results suggest a new approach and algorithm for obtaining the CNOP for a large-scale optimization problem.
文摘In this paper, Homotopy perturbation method is used to find the approximate solution of the optimal control of linear systems. In this method the initial approximations are freely chosen, and a Homotopy is constructed with an embedding parameter , which is considered as a “small parameter”. Some examples are given in order to find the approximate solution and verify the efficiency of the proposed method.
基金Acknowledgments. The authors are grateful to Professor Zhiming Wang of East China Normal University for his comments which improved the presentation of the paper. The research was supported by the National Natural Science Foundation of China （11071075, 30921064, 90820307）, Natural Science Foundation of Shanghai （10ZR1409200）, E-Institutes of Shanghai Municipal Education Commission （E03004）, the Knowledge Innovation Program of the Chinese Academy of Sciences.
文摘The existence of step-like contrast structure for a class of singularly perturbed optimal control problem is presented by contrast structure theory. By means of direct scheme of boundary function method, we construct the uniformly valid asymptotic solution for the singularly perturbed optimal control problem. As an application, an example is given to illustrate the main result in this paper.
基金the National Natural Science Foundation of China(Grant Nos.10771224,10601070)the Guangdong Provincial Natural Science Foundation of China(Grant No.05003308)+1 种基金MOE Project of Key Research Institute of Humanities and Social Sciences at UniversitiesChina-France-Russia Mathematics Collaboration(Grant No.34000-3275100)
文摘In this paper we establish a high order finite volume method for the fourth order singular perturbation problems.In conjunction with the optimal meshes,the numerical solutions resulting from the method have optimal convergence order.Numerical experiments are presented to verify our theoretical estimates.
文摘借助庞特里亚金最大值原理(Pontryagin′s Maximal Principle,PMP),将月球燃耗最优软着陆问题转化为终端时间自由型两点边值问题(Two Point Boundary Value Problem,TPBVP)。采用一种基于初值猜测技术的线性摄动法求解TPBVP,得到最优软着陆轨迹。仿真结果表明,初值猜测技术得出的伴随变量初值均落在线性摄动法的收敛区间内,收敛速度快,优化精度高。最后研究了不同制动推力大小对软着陆性能的影响,结论为:增大制动发动机推力,既可缩短软着陆的时间,又能减少软着陆的燃料消耗。
