We consider large-scale fading precoding (LSFP), which is a two-layer precoding scheme in the downlink of multi-cell massive MIMO (multiple-input multiple-output) systems to suppress inter-cell interference. We obtain the closed-form spectral efficiency (SE) with LSFP at the central network controller and maximum ratio precoding at the base stations (BSs) using the linear minimum mean-squared error or least squares channel estimators. The LSFP weights are designed based on the long-term channel statistics and two important performance metrics are optimized under the per-BS transmit power constraints. These metrics are sum SE and proportional fairness, where the resulting optimization problems are non-convex. Two efficient algorithms are developed to solve these problems by using the weighted minimum mean-squared error and the alternating direction method of multipliers methods. Moreover, two partial LSFP schemes are proposed to reduce the fronthaul signaling requirements. Simulations quantify the performance improvement of LSFP over standard single-layer precoding schemes and identify the specific advantage of each optimization problem.