@ARTICLE\{IMM2004-01448,
    author       = "K. Madsen and J. S{\o}ndergaard",
    title        = "Convergence of Hybrid Space Mapping Algorithms",
    year         = "2004",
    month        = "jun",
    keywords     = "nonlinear optimization, space mapping, global convergence",
    pages        = "145-156",
    journal      = "Optimization and Engineering",
    volume       = "5",
    editor       = "",
    number       = "2",
    publisher    = "Kluwer Academic Publishers",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/1448-full.html",
    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 \$\backslash\$circ f\$ where \$H: \$\backslash\$dR\^m \$\backslash\$mapsto \$\backslash\$dR\$ is convex and \$f: \$\backslash\$dR\^n \$\backslash\$mapsto \$\backslash\$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 \$\backslash\$circ f\$."
}