In this paper, we present a new line search and trust region algorithm for unconstrained optimization problems. The trust region center locates at somewhere in the negative gradient direction with the current best ite...In this paper, we present a new line search and trust region algorithm for unconstrained optimization problems. The trust region center locates at somewhere in the negative gradient direction with the current best iterative point being on the boundary. By doing these, the trust region subproblems are constructed at a new way different with the traditional ones. Then, we test the efficiency of the new line search and trust region algorithm on some standard benchmarking. The computational results reveal that, for most test problems, the number of function and gradient calculations are reduced significantly.展开更多
In this paper, we propose and analyze a non-monotone trust region method with non-monotone line search strategy for unconstrained optimization problems. Unlike the traditional non-monotone trust region method, our alg...In this paper, we propose and analyze a non-monotone trust region method with non-monotone line search strategy for unconstrained optimization problems. Unlike the traditional non-monotone trust region method, our algorithm utilizes non-monotone Wolfe line search to get the next point if a trial step is not adopted. Thus, it can reduce the number of solving sub-problems. Theoretical analysis shows that the new proposed method has a global convergence under some mild conditions.展开更多
In this paper, we investigate the elastic wave full-waveform inversion (FWI) based on the trust region method. The FWI is an optimization problem of minimizing the misfit between the observed data and simulated data. ...In this paper, we investigate the elastic wave full-waveform inversion (FWI) based on the trust region method. The FWI is an optimization problem of minimizing the misfit between the observed data and simulated data. Usually</span><span style="font-family:"">,</span><span style="font-family:""> the line search method is used to update the model parameters iteratively. The line search method generates a search direction first and then finds a suitable step length along the direction. In the trust region method, it defines a trial step length within a certain neighborhood of the current iterate point and then solves a trust region subproblem. The theoretical methods for the trust region FWI with the Newton type method are described. The algorithms for the truncated Newton method with the line search strategy and for the Gauss-Newton method with the trust region strategy are presented. Numerical computations of FWI for the Marmousi model by the L-BFGS method, the Gauss-Newton method and the truncated Newton method are completed. The comparisons between the line search strategy and the trust region strategy are given and show that the trust region method is more efficient than the line search method and both the Gauss-Newton and truncated Newton methods are more accurate than the L-BFGS method.展开更多
文摘In this paper, we present a new line search and trust region algorithm for unconstrained optimization problems. The trust region center locates at somewhere in the negative gradient direction with the current best iterative point being on the boundary. By doing these, the trust region subproblems are constructed at a new way different with the traditional ones. Then, we test the efficiency of the new line search and trust region algorithm on some standard benchmarking. The computational results reveal that, for most test problems, the number of function and gradient calculations are reduced significantly.
文摘In this paper, we propose and analyze a non-monotone trust region method with non-monotone line search strategy for unconstrained optimization problems. Unlike the traditional non-monotone trust region method, our algorithm utilizes non-monotone Wolfe line search to get the next point if a trial step is not adopted. Thus, it can reduce the number of solving sub-problems. Theoretical analysis shows that the new proposed method has a global convergence under some mild conditions.
文摘In this paper, we investigate the elastic wave full-waveform inversion (FWI) based on the trust region method. The FWI is an optimization problem of minimizing the misfit between the observed data and simulated data. Usually</span><span style="font-family:"">,</span><span style="font-family:""> the line search method is used to update the model parameters iteratively. The line search method generates a search direction first and then finds a suitable step length along the direction. In the trust region method, it defines a trial step length within a certain neighborhood of the current iterate point and then solves a trust region subproblem. The theoretical methods for the trust region FWI with the Newton type method are described. The algorithms for the truncated Newton method with the line search strategy and for the Gauss-Newton method with the trust region strategy are presented. Numerical computations of FWI for the Marmousi model by the L-BFGS method, the Gauss-Newton method and the truncated Newton method are completed. The comparisons between the line search strategy and the trust region strategy are given and show that the trust region method is more efficient than the line search method and both the Gauss-Newton and truncated Newton methods are more accurate than the L-BFGS method.
基金The National Natural Science Foundation of China (10231060)the Special Research Fund of Doctoral Program of Higher Education of China (20040319003)the Graduates' Creative Project of Jiangsu Province,China.
