Continuous-time proximal gradient and Douglas-Rachford splitting flows are shown to be globally exponentially stable using integral quadratic constraints, with explicit rates.
A Dynamical Systems Perspective on Nesterov Acceleration
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abstract
We present a dynamical system framework for understanding Nesterov's accelerated gradient method. In contrast to earlier work, our derivation does not rely on a vanishing step size argument. We show that Nesterov acceleration arises from discretizing an ordinary differential equation with a semi-implicit Euler integration scheme. We analyze both the underlying differential equation as well as the discretization to obtain insights into the phenomenon of acceleration. The analysis suggests that a curvature-dependent damping term lies at the heart of the phenomenon. We further establish connections between the discretized and the continuous-time dynamics.
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2019 1verdicts
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Proximal gradient flow and Douglas-Rachford splitting dynamics: global exponential stability via integral quadratic constraints
Continuous-time proximal gradient and Douglas-Rachford splitting flows are shown to be globally exponentially stable using integral quadratic constraints, with explicit rates.