A new partially parallel splitting algorithm with proximal terms for solving three-block variable linear constraints convex optimization problem

A new partially parallel splitting algorithm is proposed to solve the linear equality constrained convex optimization problem with three variables. One of the methods to solve this problem is a varying ADMM-based prediction-correction method (VAPCM), which is a partially parallel splitting algorithm with relaxation step. A new algorithm N-VAPCM is proposed based on VAPCM, which adds proximal terms to the two sub-problems of parallel computation and relax the two variables, so that its step size range is more relaxed than VAPCM. At the same time, the convergence of the new algorithm is also established. Numerical simulation results show that the N-VAPCM improves by at least 60% compared with the original algorithm for different scale calculation problems, and N-VAPCM can outperform the original algorithm by at least 50% in high-precision experiments. The computational efficiency of the new algorithm is competitive.