Convergence of Hybrid Space Mapping Algorithms

Abstract

The 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 ○ f where H : R^m → R is convex and f : Rⁿ → R^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 ○ f.