On the global and linear convergence of direct extension of ADMM for 3-block separable convex minimization models

Abstract

Abstract In this paper, we show that when the alternating direction method of multipliers (ADMM) is extended directly to the 3-block separable convex minimization problems, it is convergent if one block in the objective possesses sub-strong monotonicity which is weaker than strong convexity. In particular, we estimate the globally linear convergence rate of the direct extension of ADMM measured by the iteration complexity under some additional conditions.

Keywords

• linear convergence rate
• separable convex optimization
• alternating direction method of multiplier
• Karush-Kuhn-Tucher (KKT) system
• strong monotonicity