Optimization Algorithm Design via Electric Circuits

TL;DR

This paper introduces a new methodology for designing convex optimization algorithms inspired by electric RLC circuits, enabling automated discretization and convergence guarantees for a wide range of algorithms.

Contribution

It presents a novel circuit-inspired approach to convex optimization algorithm design, combining continuous dynamics with automated discretization for provable convergence.

Findings

Recovers many classical optimization algorithms

Enables rapid design of new algorithms with guarantees

Provides a systematic circuit-based framework for optimization

Abstract

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.