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Convergence is a well-known issue for space mapping (SM) optimization algorithms. One possible convergence safeguard is the trust region (TR) approach where the surrogate model is optimized in a restricted neighborhood of the current iteration point. We demonstrate that although formal conditions for applying trust regions are not strictly satisfied for SM surrogate models, TR improves the stability and convergence properties of the SM optimization process. Further improvement can be realized when approximate fine model Jacobian information is exploited in the construction of the SM surrogate.