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A Framework for Managing Approximation in Nonlinear Optimization

David Serafini

Presented at the 1997 CRPC Annual Meeting Poster Session

One of the leading problems in the application of standard optimization methods to real-world engineering problems is that the computation of the objective function often takes so much computer time (sometimes hours) that traditional optimization techniques are not practical. A solution that has long been used in this situation has been to approximate the objective function with something much cheaper to compute, called a "model", and optimize the model function instead of the actual objective function. This simple approach succeeds some of the time, but often fails because there is not sufficient a priori knowledge to build an adequate model. One way to address this problem is to build the model with whatever a priori knowledge is available, and during the optimization process sample the true objective at points where the model predicts decrease and use the results to adapt the model in the region of interest. A general algorithmic framework for methods of this type, called model management methods, has been developed. The framework is based on the convergence theory for pattern search methods. It specifies precise conditions under which a model management method can be guaranteed to converge, and is designed to facilitate the reuse of existing modeling and optimization software.