Configuring hybrid precoders and combiners is the main challenge to be solved to operate at millimeter wave (mmWave) frequencies. The use of hybrid architectures imposse hardware constraints on the analog precoder that need to be carefully dealt with. In this paper, we develop hybrid precoders and combiners aiming at minimizing the Euclidean distance with respect to the approximate all-digital precoders and combiners maximizing the spectral efficiency under per-antenna power constraints. Numerical results demonstrate the effectiveness of the proposed design method, whose performance is close to that of the all-digital solution.