Daniel Robinson, Johns Hopkins University

Abstract

We derive differential equations that model the continuous limit of the iterate sequence generated by the alternating direction method of multipliers (ADMM), as well as an accelerated variant. The dynamical system associated with the accelerated variant corresponds to a nonlinear generalization of a damped harmonic oscillator. We employ the direct method of Lyapunov to analyze the stability of critical points and to obtain convergence rates. Our results strengthen the connection between commonly used optimization algorithms and continuous dynamical systems. 

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