In this paper, we propose a retrospective filter trust region algorithm for unconstrained optimization, which is based on the framework of the retrospective trust region method and associated with the technique of the...In this paper, we propose a retrospective filter trust region algorithm for unconstrained optimization, which is based on the framework of the retrospective trust region method and associated with the technique of the multi-dimensional filter. The new algorithm gives a good estimation of trust region radius, relaxes the condition of accepting a trial step for the usual trust region methods. Under reasonable assumptions, we analyze the global convergence of the new method and report the preliminary results of numerical tests. We compare the results with those of the basic trust region algorithm, the filter trust region algorithm and the retrospective trust region algorithm, which shows the effectiveness of the new algorithm.展开更多
A class of nonmonotone trust region algorithms is presented for unconstrained optimizations. Under suitable conditions, the global and Q quadratic convergences of the algorithm are proved. Several rules of choosing tr...A class of nonmonotone trust region algorithms is presented for unconstrained optimizations. Under suitable conditions, the global and Q quadratic convergences of the algorithm are proved. Several rules of choosing trial steps and trust region radii are also discussed.展开更多
We propose a retrospective trust region algorithm with the trust region converging to zero for the unconstrained optimization problem. Unlike traditional trust region algo- rithms, the algorithm updates the trust regi...We propose a retrospective trust region algorithm with the trust region converging to zero for the unconstrained optimization problem. Unlike traditional trust region algo- rithms, the algorithm updates the trust region radius according to the retrospective ratio, which uses the most recent model information. We show that the algorithm preserves the global convergence of traditional trust region algorithms. The superlinear convergence is also proved under some suitable conditions.展开更多
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
文摘In this paper, we propose a retrospective filter trust region algorithm for unconstrained optimization, which is based on the framework of the retrospective trust region method and associated with the technique of the multi-dimensional filter. The new algorithm gives a good estimation of trust region radius, relaxes the condition of accepting a trial step for the usual trust region methods. Under reasonable assumptions, we analyze the global convergence of the new method and report the preliminary results of numerical tests. We compare the results with those of the basic trust region algorithm, the filter trust region algorithm and the retrospective trust region algorithm, which shows the effectiveness of the new algorithm.
文摘A class of nonmonotone trust region algorithms is presented for unconstrained optimizations. Under suitable conditions, the global and Q quadratic convergences of the algorithm are proved. Several rules of choosing trial steps and trust region radii are also discussed.
文摘We propose a retrospective trust region algorithm with the trust region converging to zero for the unconstrained optimization problem. Unlike traditional trust region algo- rithms, the algorithm updates the trust region radius according to the retrospective ratio, which uses the most recent model information. We show that the algorithm preserves the global convergence of traditional trust region algorithms. The superlinear convergence is also proved under some suitable conditions.
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.
