Continuous-time proximal gradient and Douglas-Rachford splitting flows are shown to be globally exponentially stable using integral quadratic constraints, with explicit rates.
On the exponential convergence rate of proximal gradient flow algorithms,
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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.