Inexact generalized ADMM with relative error criteria for linearly constrained convex optimization problems.

The alternating direction method of multipliers (ADMM) and its variants are widely used in solving practical problems. However, the efficiency of such methods largely relies on the solvability of involving subproblems. In this paper, we propose two types of inexact generalized proximal ADMM with different relative error criteria to solve the linearly constrained separable convex minimization problems. The relative error criteria are only controlled by several certain constants in range of [0, 1). The convergence and ergodic iteration-complexity bound of the new methods are rigorously established. Moreover, some numerical results on ℓ 1 -regularized sparse recovery and image deblurring problems are reported to illustrate the advantages of the new methods. [ABSTRACT FROM AUTHOR]