This letter introduces a novel approach to flexible precoding in multi-user wireless communications with movable antennas (MAs). The authors propose a sparse optimization (SO) framework based on regularized zero-forcing (RZF) to optimize antenna positions and precoding matrices, aiming to minimize inter-user interference and transmit power. They introduce an off-grid regularized least squares-based orthogonal matching pursuit (RLS-OMP) method to efficiently solve the SO problem. The proposed method leverages subspace projection to optimize antenna positions, enhancing the system's sum rate by more than twice compared to fixed antenna positions. The effectiveness of the proposed approach is demonstrated through simulations, showing superior performance in various scenarios, including different movable regions, number of channel paths, and antenna positions. The letter provides a comprehensive framework for optimizing antenna positions in MAs, offering new insights and practical solutions for multi-user wireless communications.This letter introduces a novel approach to flexible precoding in multi-user wireless communications with movable antennas (MAs). The authors propose a sparse optimization (SO) framework based on regularized zero-forcing (RZF) to optimize antenna positions and precoding matrices, aiming to minimize inter-user interference and transmit power. They introduce an off-grid regularized least squares-based orthogonal matching pursuit (RLS-OMP) method to efficiently solve the SO problem. The proposed method leverages subspace projection to optimize antenna positions, enhancing the system's sum rate by more than twice compared to fixed antenna positions. The effectiveness of the proposed approach is demonstrated through simulations, showing superior performance in various scenarios, including different movable regions, number of channel paths, and antenna positions. The letter provides a comprehensive framework for optimizing antenna positions in MAs, offering new insights and practical solutions for multi-user wireless communications.