A trust-region strategy for manifold mapping optimization.

As a starting point we take the space-mapping iteration technique by Bandler et al. for the efficient solution of optimization problems. This technique achieves acceleration of accurate design processes with the help of simpler, easier to optimize models. We observe the difference between the solution of the optimization problem and the computed space-mapping solutions. We repair this discrepancy by exploiting the correspondence with defect-correction iteration and we construct the manifold-mapping algorithm, which is as efficient as the space-mapping algorithm but converges to the exact solution. To increase the robustness of the algorithm we also introduce a trust-region strategy that is based on the generalized singular value decomposition of the linearized fine and coarse manifold representations. The effect of the strategy is shown by the solution of a variety of small non-linear least squares problems