Convergence of Hybrid Space Mapping Algorithms



AbstractThe space mapping technique is intended for optimization of engineering models which involve very expensive function evaluations. It may be considered a preprocessing method which often provides a very efficient initial phase of an optimization procedure. However, the ultimate rate of convergence may be poor, or the method may even fail to converge to a stationary point.
We consider a convex combination of the space mapping technique with a classical optimization technique. The function to be optimized has the form $H \circ f$ where $H: \dR^m \mapsto \dR$ is convex and $f: \dR^n \mapsto \dR^m$ is smooth. Experience indicates that the combined method maintains the initial efficiency of the space mapping technique. We prove that the global convergence property of the classical technique is also maintained: The combined method provides convergence to the set of stationary points of $H \circ f$.
Keywordsnonlinear optimization, space mapping, global convergence
TypeJournal paper [With referee]
JournalOptimization and Engineering
Year2004    Month June    Vol. 5    No. 2    pp. 145-156
PublisherKluwer Academic Publishers
BibTeX data [bibtex]
IMM Group(s)Scientific Computing


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