Parallel Splitting Method For Solving Multi-block Separable Convex Optimization Problems

Alternating direction method of multipliers(ADMM)is widely used in convex optimization problems.It plays an important role in image processing,machine learning,signal processing and other fields.When the multi-block separable convex optimization problem contains two groups of variables,the sequence generated by ADMM is convergent.In practice,it performs well for solving numerical experi-ments.With the development of big data and artificial intelligence,the scale of the problem is expanding,and the variables in the objective function are much larger than two groups.Existing research results show that the directly extended AD-MM does not converge.There are mainly two kinds of methods to preserve the advantage of the directly extended ADMM algorithm in numerical experiments,and at the same time ensure the convergence of the iterative sequence generated by the algorithm.One method is to reinforce the objective function of the problem,such as the objective function is strongly convex or partially strongly convex.Another method is to modify the ADMM by adding correction steps to make the iterative sequence converge.This paper proposes a new block parallel ADMM algorithm with correction step.During the process of each iteration,the variables are grouped,updated se?rially within groups and solved parallelly between groups.The advantage of this algorithm is to minimize the time required for the computation while the latest it?eration information can be used as much as possible.In this paper,the convergence of the algorithm is analyzed,the method of selecting parameters of the algorithm are given to ensure the corresponding matrix of positive definite matrix,finally the algorithm is applied to the concrete problem,numerical experiments are given to verify the effectiveness of the algorithm.