The paper studies the multi-user precoding problem as a non-convex optimization problem for wireless multiple inputs and multiple outputs (MIMO) systems. In our work, we approximate the target Spectral Efficiency function with a novel computationally simpler function. Then, we reduce the precoding problem to an unconstrained optimization task using a special differential projection method and solve it by the Quasi-Newton L-BFGS iterative procedure to achieve gains in capacity. We are testing the proposed approach in several scenarios generated using Quadriga-open-source software for generating realistic radio channel impulse response. Our method shows monotonic improvement over heuristic methods with reasonable computation time. The proposed L-BFGS optimization scheme is novel in this area and shows a significant advantage over the standard approaches. The proposed method has simple implementation and can be a good reference for other heuristic algorithms in this field. © 2022 Informa UK Limited, trading as Taylor & Francis Group.