论文标题
黑森州近似值
Hessian approximations
论文作者
论文摘要
这项工作介绍了嵌套的Hessian近似值，这是一种二阶近似方法，可用于任何需要此类信息的无衍生优化例程中。它建立在广义的简单梯度的基础上，并被证明具有误差绑定，该误差限制在其结构中使用的两组的最大半径。我们表明，当嵌套集合的Hessian计算中使用的点具有有利的结构时，（n+1）（n+2）/2功能评估足以近似于Hessian。但是，嵌套的Hessian还允许使用更多点的评估集，而无需否定错误分析。开发了两种基于微积分的Hessian的近似技术，并证明了这两种优势。
This work introduces the nested-set Hessian approximation, a second-order approximation method that can be used in any derivative-free optimization routine that requires such information. It is built on the foundation of the generalized simplex gradient and proved to have an error bound that is on the order of the maximal radius of the two sets used in its construction. We show that when the points used in the computation of the nested-set Hessian have a favourable structure, (n+1)(n+2)/2 function evaluations are sufficient to approximate the Hessian. However, the nested-set Hessian also allows for evaluation sets with more points without negating the error analysis. Two calculus-based approximation techniques of the Hessian are developed and some advantages of the same are demonstrated.
