一种求解3块变量线性约束凸优化问题的新邻近部分平行分裂算法

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

为解决3块变量的线性等式约束凸优化问题,提出一种新的部分平行分裂算法.基于交替方向乘子法的预测校正方法(VAPCM)是解决该问题的方法之一,它是一种带有松弛步的部分平行分裂算法.现基于VAPCM提出新算法N-VAPCM,在平行计算的两个子问题中添加邻近项,并对这2块变量进行松弛,则其步长范围比VAPCM更为放松.同时建立了新算法的收敛性.数值实验结果表明,对不同规模计算问题,N-VAPCM较原算法提升至少60%,并且在高精度实验中,N-VAPCM也可以领先至少50%.新算法的计算效率是具有竞争性的.

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.