2023/05/24 by Alexander A. Davydov, Davydov, Alexander, Veronica Centorrino +7 · 2 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Peroxisome Proliferator-Activated Receptors #Signal Processing (eess.SP) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2305.15595
openalex publication_date 2023/05/24 · openalex created_date 2023/05/27 · openalex updated_date 2026/08/01
In this article, we provide a novel and broadly-applicable contraction-theoretic approach to continuous-time time-varying convex optimization. For any parameter-dependent contracting dynamics, we show that the tracking error is asymptotically proportional to the rate of change of the parameter and that the proportionality constant is upper bounded by Lipschitz constant in which the parameter appears divided by the contraction rate of the dynamics squared. We additionally establish that augmenting any parameter-dependent contracting dynamics with a feedforward prediction term ensures that the tracking error vanishes exponentially quickly. To apply these results to time-varying convex optimization, we establish the strong infinitesimal contractivity of dynamics solving three canonical problems: monotone inclusions, linear equality-constrained problems, and composite minimization problems. For each case, we derive the sharpest-known contraction rates and provide explicit bounds on the tracking error between solution trajectories and minimizing trajectories. We validate our theoretical results on two numerical examples and on an application to control barrier function-based controller design that involves real hardware.