Large-Scale Multidisciplinary Validation of Enriched Multipoint Cubic Approximations

Abstract

Previous work has demonstrated a generalized optimization method for problems with nonlinear objective and/or nonlinear constraints. The technique creates a cubic approximation based on a reduced design space of previous design points. The reduced space is enriched using the gradient information at previous design points, if available. The approximated Hessian matrix can be signi…cantly smaller than the full-space Hessian matrix, thus reducing required memory. The Enriched Multipoint Cubic Approximation is shown to accurately reproduce the function and gradient values at each previous design point. By optimizing the cubic approximation between each function evaluation, this method is expected to reduce the number of exact objective and constraint function calculations required. Test cases are demonstrated and compared to published optimization results for nonlinear objective and constraint functions. Also, the Enriched Multipoint Cubic Approximation results are compared to the state-of-the-art optimization software. This generalized optimization method does not signi…cantly increase the number of iterations required to converge to an optimum solution as the number of design variables increases.