CONVERGENCE OF TRUST REGION AUGMENTED LAGRANGIAN-METHODS USING VARIABLE FIDELITY APPROXIMATION DATA

To date the primary focus of most constrained approximate optimization strategies is that application of the method should lead to improved designs. Few researchers have focused on the development of constraine d approximate optimization strategies that are assured of converging t o a Karush-Kuhn-Tucker (KKT) point for the problem. Recent work by the authors based on a trust region model management strategy has shown p romise in managing the convergence of constrained approximate optimiza tion in application to a suite of single level optimization test probl ems. Using a trust-region model management strategy, coupled with an a ugmented Lagrangian approach for constrained approximate optimization, the authors have shown in application studies that the approximate op timization process converges to a KKT point for the problem. The appro ximate optimization strategy sequentially builds a cumulative response surface approximation of the augmented Lagrangian which is then optim ized subject to a trust region constraint. In this research the author s develop a formal proof of convergence for the response surface appro ximation based optimization algorithm. Previous application studies we re conducted on single level optimization problems for which response surface approximations were developed using conventional statistical r esponse sampling techniques such as central composite design to query a high fidelity model over the design space. In this research the auth ors extend the scope of application studies to include the class of mu ltidisciplinary design optimization (MDO) test problems. More importan tly the authors show that response surface approximations constructed from variable fidelity data generated during concurrent subspace optim izations (CSSOs) can be effectively managed by the trust region model management strategy. Results for two multidisciplinary test problems a re presented in which convergence to a KKT point is observed. The form al proof of convergence and the successful MDO application of the algo rithm using variable fidelity data generated by CSSO are original cont ributions to the growing body of research in MDO.