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
This paper presents a new nonmonotone filter line search technique in association with the MBFGS method for solving unconstrained minimization.The filter method,which is traditionally used for constrained nonlinear pr...This paper presents a new nonmonotone filter line search technique in association with the MBFGS method for solving unconstrained minimization.The filter method,which is traditionally used for constrained nonlinear programming(NLP),is extended to solve unconstrained NLP by converting the latter to an equality constrained minimization.The nonmonotone idea is employed to the filter method so that the restoration phrase,a common feature of most filter methods,is not needed.The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions.The results of numerical experiments indicate that the proposed method is efficient.展开更多
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.
基金supported by the National Science Foundation under Grant No.11371253the Science Foundation under Grant No.11C0336 of Provincial Education Department of Hunan
文摘This paper presents a new nonmonotone filter line search technique in association with the MBFGS method for solving unconstrained minimization.The filter method,which is traditionally used for constrained nonlinear programming(NLP),is extended to solve unconstrained NLP by converting the latter to an equality constrained minimization.The nonmonotone idea is employed to the filter method so that the restoration phrase,a common feature of most filter methods,is not needed.The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions.The results of numerical experiments indicate that the proposed method is efficient.
