In aerodynamic design, accurate and robust surrogate models are important to accelerate computationally expensive CFD-based optimization. Machine learning techniques can also enable affordable exploration of high-dimensional design spaces with targeted selection of sparse high-fidelity data. In this paper, a multi-fidelity global-local approach is presented and applied to the surrogate-based design optimization of a highly-loaded transonic compressor rotor. The key idea is to train multi-fidelity surrogates with fewer high-fidelity RANS predictions and more rapid and inexpensive lower-fidelity RANS evaluations. The framework also introduces a global-local search algorithm that can spin-off multiple local optimization threads over narrow and targeted design spaces, concurrently to a constantly adapting global optimization thread. The approach is demonstrated with an optimization of the transonic NASA rotor 37, yielding significant increase in performance within a dozen of optimization iterations.