Abstract: We considered the 3-block varibles convex optimization problem with linear constraints. In the partial parallel splitting algorithm (APCM), on the basis of selecting different step parameters in the correction step,  we proposed a proximal partial parallel splitting method (PAPCM), and proved the convergence of the proposed  algorithm. On the basis of selecing different step parameters in APCM, adding a proximal term to the objective function of a sub-problem, and a new parameter condition was established. Compared with  APCM, the parameter condition of the proposed algorithm was  greatly relaxed, making the algorithm more practical. Numerical results show that, compared with the existing algorithms, the iteration number and computation time of the proposed algorithm are both significantly reduced.

Key words: convex optimization, alternating direction multiplier method, partial parallel splitting algorithm, proximal term