Study On A Class Of Algorithms For Solving 3-Block Separable Convex Minimization Problems

In this paper, we present an algorithm for solving 3-block separable convex minimization problems with one coupled linear equation constraint. By choosing the semi-proximal terms properly, we establish the global linear rate of convergence of the proposed algorithm for the step-length τ ∈ (0, ((?)5+1)/2) and the penalty parameter c ∈ (0,+∞). In our analysis, we only assume that the error bound condition holds. In practical applications, the algorithm has the same splitting structure with the classic ADMM algorithm, and provides convenience for the calculation of actual problems.