论文标题
显式伪频率延续和不受约束优化的信任区域更新策略
Explicit pseudo-transient continuation and the trust-region updating strategy for unconstrained optimization
论文作者
论文摘要
本文考虑了一种明确的延续方法和无约束优化问题的信任区域更新策略。此外，为了提高其计算效率和鲁棒性，新方法使用开关预处理技术。在条件良好的阶段，新方法使用L-BFGS方法作为预处理技术，以提高其计算效率。否则，新方法将Hessian矩阵的倒数用作前调节器，以提高其鲁棒性。数值结果ASLO表明，新方法比传统优化方法（例如Trust-Region方法和线路搜索方法）更强大，更快。新方法的计算时间约为信任区域方法的一百分之一（MATLAB2019A环境的子例程fminunc.m，它是由信任区域方法设置的）或该行搜索方法的五分之一（fminunc.m是由Quasi-Newton方法设置的大规模问题）。最后，还给出了新方法的全局收敛分析。
This paper considers an explicit continuation method and the trust-region updating strategy for the unconstrained optimization problem. Moreover, in order to improve its computational efficiency and robustness, the new method uses the switching preconditioning technique. In the well-conditioned phase, the new method uses the L-BFGS method as the preconditioning technique in order to improve its computational efficiency. Otherwise, the new method uses the inverse of the Hessian matrix as the pre-conditioner in order to improve its robustness. Numerical results aslo show that the new method is more robust and faster than the traditional optimization method such as the trust-region method and the line search method. The computational time of the new method is about one percent of that of the trust-region method (the subroutine fminunc.m of the MATLAB2019a environment, it is set by the trust-region method) or one fifth of that the line search method (fminunc.m is set by the quasi-Newton method) for the large-scale problem. Finally, the global convergence analysis of the new method is also given.
