A Novel Complex-Variable Prediction-Correction Method Applied to Beamforming Design

Complex-variable matrix optimization problems are fundamental in signal processing and related engineering applications, yet existing methods often become computationally inefficient when handling high-dimensional variables and nonlinear constraints. In this paper, we propose a novel prediction-correction method for complex-variable optimization based on a variational inequality framework. This method directly operates in the complex domain and achieves an ergodic convergence rate of$\mathcal {O}(1/t)$under mild conditions. Numerical results on a practical beamforming design problem demonstrate that the proposed approach achieves comparable solution accuracy to conventional methods while reducing the computational time by more than three orders of magnitude.