In this paper, we analyze in some detail the manifold-mapping optimization technique introduced recently [Echeverría and Hemker in space mapping and defect correction. Comput Methods Appl Math 5(2): 107-–136, 2005]. Manifold mapping aims at accelerating optimal design procedures that otherwise require many evaluations of time-expensive cost functions.We give a proof of convergence for the manifold-mapping iteration. By means of two simple optimization problemswe illustrate the convergence results derived. Finally, the performances of several variants of the method are compared for some design problems from electromagnetics.

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Springer
Computing and Visualization in Science
Space-mapping and related techniques for inverse problems in magnetic shape design, with application to an electromagnetic actuator
Scientific Computing

Echeverria, D., & Hemker, P. (2008). Manifold mapping: a two-level optimization technique. Computing and Visualization in Science, 11(4-6), 193–206.