Studying the space-mapping technique by Bandler et al. [J. Bandler, R. Biernacki, S. Chen, P. Grobelny, R.H. Hemmers, Space mapping technique for electromagnetic optimization, IEEE Trans. Microwave Theory Tech. 42 (1994) 2536–2544] for the solution of optimization problems, we observe the possible difference between the solution of the optimization problem and the computed space-mapping solution. 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 introduce a trust-region strategy (a regularization technique) based on the generalized singular value decomposition of the linearized fine and coarse manifold representations. The effect of this strategy is shown by the solution of a variety of small non-linear least squares problems. Finally we show the use of the technique for a more challenging engineering problem.

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Academic Press
Journal of Computational Physics
Space-mapping and related techniques for inverse problems in magnetic shape design, with application to an electromagnetic actuator
Scientific Computing

Hemker, P.W, & Echeverria, D. (2007). A trust-region strategy for manifold-mapping optimization. Journal of Computational Physics, 224(1), 464–475.