Second-Order Corrections for Surrogate-Based Optimization with Model Hierarchies Export

@article{eldred04, abstract = {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 de- veloped 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 gradi- ents 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 correc- tions 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.}, author = {Eldred, M. S. and Giunta, A. A. and Collis, S. S.}, citeulike-article-id = {2815799}, journal = {American Institute of Aeronautics and Astronautics}, keywords = {optimisation, region-de-confiance, surface-de-reponse}, number = {4457}, posted-at = {2008-05-20 14:49:55}, priority = {0}, title = {Second-Order Corrections for Surrogate-Based Optimization with Model Hierarchies}, year = {2004} }

TY - JOUR ID - eldred04 L3 - citeulike-article-id:2815799 N2 - 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 de- veloped 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 gradi- ents 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 correc- tions 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. IS - 4457 JF - American Institute of Aeronautics and Astronautics TI - Second-Order Corrections for Surrogate-Based Optimization with Model Hierarchies KW - optimisation KW - region-de-confiance KW - surface-de-reponse AU - Eldred, MS AU - Giunta, AA AU - Collis, SS PY - 2004/// ER -