Andrew Packard — Page 2

arXiv2015

Compositional Performance Certification of Interconnected Systems using ADMM

A compositional performance certification method is presented for interconnected systems using subsystem dissipativity properties and the interconnection structure. A large-scale optimization problem is formulated to search for the most relevant dissipativity properties. The alternating direction method of multipliers (ADMM) is employed to decompose and solve this problem, and is demonstrated on several examples.

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arXiv2015

A General Analysis of the Convergence of ADMM

We provide a new proof of the linear convergence of the alternating direction method of multipliers (ADMM) when one of the objective terms is strongly convex. Our proof is based on a framework for analyzing optimization algorithms introduced in Lessard et al. (2014), reducing algorithm convergence to verifying the stability of a dynamical system. This approach generalizes a number of existing results and obviates any assumptions about specific choices of algorithm parameters. On a numerical example, we demonstrate that minimizing the derived bound on the convergence rate provides a practical approach to selecting algorithm parameters for particular ADMM instances. We complement our upper bound by constructing a nearly-matching lower bound on the worst-case rate of convergence.

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