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

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... nsistency 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.