Second-Order Corrections for Surrogate-Based Optimization with Model Hierarchies
Second-Order Corrections for Surrogate-Based Optimization with Model Hierarchies
复制标题
DOI：
10.2514/6.2004-4457
复制
发表时间：
2004-08
期刊：
影响因子：
--
通讯作者：
M. Eldred;A. Giunta;S. S. Collis-S.
中科院分区：
文献类型：
--
作者：
M. Eldred;A. Giunta;S. S. Collis-S.
基于代理的优化方法通过其驯服非光滑性和减少计算费用的能力已经成为工程设计问题的有效技术。近年来，支持的数学理论已经发展到这些方法的可证明的收敛性提供了基础。这种可证明收敛理论的要求之一涉及代理模型和它所近似的潜在真值模型之间的一致性。这种一致性可以通过各种校正方法来实现，并且在基于代理的模型层次优化的情况下尤其重要。一阶加法和乘法校正目前存在，满足在一个单一的点的真值和代理模型之间的值和梯度的一致性。本文证明了一阶一致性可能不足以在实践中实现可接受的收敛速度，并提出了新的二阶加法，乘法和组合校正，可以显着加快收敛。这些二阶修正可能会增强与实际真值模型Hessian或其有限差分、拟牛顿或高斯-牛顿近似的一致性。
Surrogate-based optimization methods have become established as effective techniques for engineering design problems through their ability to tame nonsmoothness and reduce computational expense. In recent years, supporting mathematical theory has been developed to provide the foundation of provable convergence for these methods. One of the requirements of this provable convergence theory involves consistency between the surrogate model and the underlying truth model that it approximates. This consistency can be enforced through a variety of correction approaches, and is particularly essential in the case of surrogate-based optimization with model hierarchies. First-order additive and multiplicative corrections currently exist which satisfy consistency in values and gradients between the truth and surrogate models at a single point. This paper demonstrates that first-order consistency can be insufficient to achieve acceptable convergence rates in practice and presents new second-order additive, multiplicative, and combined corrections which can significantly accelerate convergence. These second-order corrections may enforce consistency with either the actual truth model Hessian or its finite difference, quasi-Newton, or Gauss-Newton approximation.