Iteration Complexity of the Alternating Direction Method of Multipliers for Quasi-Separable Problems in Multi-Disciplinary Design Optimization

The Alternating Direction Method of Multipliers (ADMM) is a distributed algorithm suitable for quasi-separable problems in Multi-disciplinary Design Optimization. Previous authors have studied the convergence and complexity of the ADMM algorithm by treating it as an instance of the proximal point algorithm. In this paper, those previous results are extended to an alternate form of the ADMM algorithm applied to the quasi-separable problem. Secondly, a dynamic penalty parameter updating heuristic for the ADMM algorithm is introduced and compared against a previously proposed updating heuristic. The proposed updating heuristic was tested on a distributed linear model fitting example and performed favorably against the other heuristic and the fixed penalty parameter scheme.