Optimization Algorithm Design via Electric Circuits
This approach provides a systematic way for researchers and practitioners to design and analyze optimization algorithms, though it appears incremental as it builds on existing circuit analogies.
The authors tackled the problem of designing convex optimization algorithms by introducing a methodology that uses electric RLC circuits to model continuous-time dynamics, which are then discretized to create provably convergent discrete-time algorithms, enabling the recovery of classical methods and exploration of new ones.
We present a novel methodology for convex optimization algorithm design using ideas from electric RLC circuits. Given an optimization problem, the first stage of the methodology is to design an appropriate electric circuit whose continuous-time dynamics converge to the solution of the optimization problem at hand. Then, the second stage is an automated, computer-assisted discretization of the continuous-time dynamics, yielding a provably convergent discrete-time algorithm. Our methodology recovers many classical (distributed) optimization algorithms and enables users to quickly design and explore a wide range of new algorithms with convergence guarantees.