This paper introduces a flexible precoding scheme for multi-user communications with movable antennas (MAs), focusing on regularized zero-forcing (RZF) precoding through sparse optimization (SO). The proposed method optimizes both antenna positions and the precoding matrix to minimize inter-user interference and transmit power. A novel off-grid regularized least squares-based orthogonal matching pursuit (RLS-OMP) algorithm is introduced for this purpose. The method is analyzed from a subspace projection perspective, revealing that optimizing antenna positions is equivalent to finding an optimal subspace spanned by the array-position manifolds. The proposed flexible precoding scheme achieves a sum rate that exceeds more than twice that of fixed antenna positions. The paper discusses the potential of MAs in enhancing wireless communications by dynamically adjusting antenna positions to improve channel conditions. It reviews prior research on dynamic antenna position optimization techniques, including antenna selection (AS) and array synthesis. The study also explores the performance of MAs in various scenarios, including point-to-point communications and uplink power minimization. The system model considers a multi-user multiple-input single-output (MU-MISO) downlink system with movable antennas. The received signal at each user is modeled based on the channel, precoding matrix, and noise. The paper presents a flexible RZF precoding framework that incorporates antenna position optimization, leading to improved performance in terms of sum rate. The proposed SO-based flexible RZF precoding method is formulated as an optimization problem with constraints on antenna positions. The method is implemented through an iterative process that identifies and optimizes the most suitable antenna positions, followed by residual calculation and support confirmation. The algorithm is validated through simulation results, showing that flexible precoding outperforms fixed antenna position and fast antenna selection methods in terms of sum rate. The paper concludes that the proposed flexible RZF precoding scheme offers significant improvements in performance compared to traditional fixed antenna systems and provides new insights into the potential of MAs in wireless communications. The method is shown to be effective in various scenarios, including different channel conditions and antenna configurations.This paper introduces a flexible precoding scheme for multi-user communications with movable antennas (MAs), focusing on regularized zero-forcing (RZF) precoding through sparse optimization (SO). The proposed method optimizes both antenna positions and the precoding matrix to minimize inter-user interference and transmit power. A novel off-grid regularized least squares-based orthogonal matching pursuit (RLS-OMP) algorithm is introduced for this purpose. The method is analyzed from a subspace projection perspective, revealing that optimizing antenna positions is equivalent to finding an optimal subspace spanned by the array-position manifolds. The proposed flexible precoding scheme achieves a sum rate that exceeds more than twice that of fixed antenna positions. The paper discusses the potential of MAs in enhancing wireless communications by dynamically adjusting antenna positions to improve channel conditions. It reviews prior research on dynamic antenna position optimization techniques, including antenna selection (AS) and array synthesis. The study also explores the performance of MAs in various scenarios, including point-to-point communications and uplink power minimization. The system model considers a multi-user multiple-input single-output (MU-MISO) downlink system with movable antennas. The received signal at each user is modeled based on the channel, precoding matrix, and noise. The paper presents a flexible RZF precoding framework that incorporates antenna position optimization, leading to improved performance in terms of sum rate. The proposed SO-based flexible RZF precoding method is formulated as an optimization problem with constraints on antenna positions. The method is implemented through an iterative process that identifies and optimizes the most suitable antenna positions, followed by residual calculation and support confirmation. The algorithm is validated through simulation results, showing that flexible precoding outperforms fixed antenna position and fast antenna selection methods in terms of sum rate. The paper concludes that the proposed flexible RZF precoding scheme offers significant improvements in performance compared to traditional fixed antenna systems and provides new insights into the potential of MAs in wireless communications. The method is shown to be effective in various scenarios, including different channel conditions and antenna configurations.