We introduce a two-stage global-then-local search method for solving feasibility problems. The approach pairs the advantageous global tendency of the Douglas–Rachford method to find a basin of attraction for a fixed point, together with the local tendency of the circumcentered reflections method to perform faster within such a basin. We experimentally demonstrate the success of the method for solving nonconvex problems in the context of wavelet construction formulated as a feasibility problem. References