A Trust Region Framework for Managing Approximation Models in Engineering Optimization

We describe an approach to managing the use of approximate models in optimization. This approach combines the idea of approximation models from engineering design optimization with the model trust region approach from nonlinear programming. The trust region framework regulates the amount of optimization done with the approximate models before one needs to appeal to a detailed model to check the validity of the design generated using the approximate models. This regulation is based on the ability of the approximations to predict the true behavior of the system being optimized. The method we propose inherits all the convergence analysis and robustness of classical trust region algorithms for nonlinear optimization. Introduction We describe an approach to managing the use of approximate models in optimization. Our approach combines the idea of approximation models from engineering design optimization 1] with the model trust region approach from nonlinear programming 2]. The use of approximate models reduces the computational cost incurred when running a numerical optimization procedure. The trust region framework gives an adaptive method for managing the amount of optimization done with the approximate models before one needs to use a detailed model to check the validity of the design generated using the approximate models. This regulation is based on the ability of the approximations to predict the true behavior of