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Convergence Analysis and Design of Multi-block ADMM via Switched Control Theory by Li, Jun; Liu, Hongfu; Wu, Yue; Fu, Yun is a scholarly article available to read on EtoBox.

What is Convergence Analysis and Design of Multi-block ADMM via Switched Control Theory about?

We consider three challenges in multi-block Alternating Direction Method of Multipliers (ADMM): building convergence conditions for ADMM with any block (variable) sequence, finding available block sequences to be fit for ADMM, and designing useful parameter controllers for ADMM with unfixed parameters. To address these challenges, we develop a switched control framework for studying multi-block ADMM. First, since ADMM recursively and alternately updates the block-variables, it is converted into a discrete-time switched dynamical system. Second, we study exponential stability and stabilizability of the switched system for linear convergence analysis and design of ADMM by employing switched Lyapunov functions. Moreover, linear matrix inequalities conditions are proposed to ensure convergence of ADMM under arbitrary sequence, to find convergent sequences, and to design the fixed parameters. These conditions are checked and solved by employing semidefinite programming. Numerical experiments further verify the effectiveness of our proposed theories.

Author

Li, Jun; Liu, Hongfu; Wu, Yue; Fu, Yun

Published

2017

Language

EN