求解三块变量约束凸优化问题的邻近部分平行分裂算法

考虑线性约束三块变量的凸优化问题，在部分平行分裂算法中选取不同步长参数的基础上，提出一种邻近部分平行分裂算法，并证明该算法的收敛性.该算法通过在部分平行分裂算法中选取不同步长参数的基础上，在一个子问题的目标函数中加入邻近项，建立新的参数条件.与部分平行分裂算法相比，该算法极大放松了参数条件，使算法更具实用性.数值实验结果表明，与已有算法相比，该算法的迭代次数和计算时间均显著下降.

Proximal Partial Parallel Splitting Algorithm for Solving Three Block Variable Constrained Convex Optimization Problems

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.