Abstract:

In this paper, we indicate the reason of divergence, and illustrate the strategies which modify the alternating direction method of multipliers (ADMM) to a convergent one for the linearly constrained separable convex optimization with three individual functions. Finally, using a uniform framework, we give the simple proofs for the convergence and O(1/t) convergence rate in the ergodic sense of the ADMM-like methods.

Key words: convex optimization, splitting contraction methods, variational inequality, uniform framework, convergence rate