Manifold mapping: a two-level optimization technique

In this paper, we analyze in some detail the manifold-mapping optimization technique introduced recently [Echeverria 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 problems we illustrate the convergence results derived. Finally, the performances of several variants of the method are compared for some design problems from electromagnetics.