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
Full waveform inversion( FWI) is a challenging data-fitting procedure between model wave field value and theoretical wave field value. The essence of FWI is an optimization problem,and therefore,it is important to stu...Full waveform inversion( FWI) is a challenging data-fitting procedure between model wave field value and theoretical wave field value. The essence of FWI is an optimization problem,and therefore,it is important to study optimization method. The study is based on conventional Memoryless quasi-Newton( MLQN)method. Because the Conjugate Gradient method has ultra linear convergence,the authors propose a method by using Fletcher-Reeves( FR) conjugate gradient information to improve the search direction of the conventional MLQN method. The improved MLQN method not only includes the gradient information and model information,but also contains conjugate gradient information. And it does not increase the amount of calculation during every iterative process. Numerical experiment shows that compared with conventional MLQN method,the improved MLQN method can guarantee the computational efficiency and improve the inversion precision.展开更多
Minimax programming problems involving generalized （p, r）-invex functions are consid- ered. Parametric sufficient optimality conditions and duality results are established under the aforesaid assumptions on the obje...Minimax programming problems involving generalized （p, r）-invex functions are consid- ered. Parametric sufficient optimality conditions and duality results are established under the aforesaid assumptions on the objective and constraint functions.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.
文摘Full waveform inversion( FWI) is a challenging data-fitting procedure between model wave field value and theoretical wave field value. The essence of FWI is an optimization problem,and therefore,it is important to study optimization method. The study is based on conventional Memoryless quasi-Newton( MLQN)method. Because the Conjugate Gradient method has ultra linear convergence,the authors propose a method by using Fletcher-Reeves( FR) conjugate gradient information to improve the search direction of the conventional MLQN method. The improved MLQN method not only includes the gradient information and model information,but also contains conjugate gradient information. And it does not increase the amount of calculation during every iterative process. Numerical experiment shows that compared with conventional MLQN method,the improved MLQN method can guarantee the computational efficiency and improve the inversion precision.
文摘Minimax programming problems involving generalized （p, r）-invex functions are consid- ered. Parametric sufficient optimality conditions and duality results are established under the aforesaid assumptions on the objective and constraint functions.
