The purpose of this paper is extending the convergence analysis of Han and Yuan (2012) for alternating direction method of multipliers (ADMM) from the strongly convex to a more general case. Under the assumption that the individual functions are composites of strongly convex functions and linear functions, we prove that the classical ADMM for separable convex programming with two blocks can be extended to the case with more than three blocks. The problems, although still very special, arise naturally from some important applications, for example, route-based traffic assignment problems.
"Convergence Analysis of Alternating Direction Method of Multipliers for a Class of Separable Convex Programming." Abstr. Appl. Anal. 2013 (SI54) 1 - 8, 2013. https://doi.org/10.1155/2013/680768