TRUST REGION AUGMENTED LAGRANGIAN-METHODS FOR SEQUENTIAL RESPONSE-SURFACE APPROXIMATION AND OPTIMIZATION

A common engineering practice is the use of approximation models in pl ace of expensive computer simulations to drive a multidisciplinary des ign process based on nonlinear programming techniques. The use of appr oximation strategies is designed to reduce the number of detailed, cos tly computer simulations required during optimization while maintainin g the pertinent features of the design problem. To date the primary fo cus of most approximate optimization strategies is that application of the method should lead to improved designs. This is a laudable attrib ute and certainly relevant for practicing designers. However to date f ew researchers have focused on the development of approximate optimiza tion strategies that are assured of converging to a solution of the or iginal problem. Recent works based on trust region model management st rategies have shown promise in managing convergence in unconstrained a pproximate minimization. In this research we extend these well establi shed notions from the literature on trust-region methods to manage the convergence of the more general approximate optimization problem wher e equality, inequality and variable bound constraints are present. The primary concern addressed in this study is how to manage the interact ion between the optimization and the fidelity of the approximation mod els to ensure that the process converges to a solution of the original constrained design problem. Using a trust-region model management str ategy coupled with an augmented Lagrangian approach for constrained ap proximate optimization, one can show that the optimization process con verges to a solution of the original problem. In this research an appr oximate optimization strategy is developed in which a cumulative respo nse surface approximation of the augmented Lagrangian is sequentially optimized subject to a trust region constraint. Results for several te st problems are presented in which convergence to a Karush-kuhn-Tucker (KKT) point is observed.