用电路模型设计可证明收敛的优化算法
Optimization Algorithm Design via Electric Circuits
- 基于RLC电路构建连续动态系统，模拟优化问题求解过程
- 自动离散化电路方程，生成带收敛保证的离散算法
- 可快速设计新算法，适合算法设计与理论研究者
我们提出一种基于电学RLC电路的凸优化算法设计新方法。首先，为给定优化问题设计一个合适的电路，其连续时间动态系统能收敛到该问题的解；其次，通过计算机辅助对连续动态进行自动离散化，得到一个具有收敛性保证的离散算法。该方法可复现多种经典（分布式）优化算法，并使用户能快速设计和探索大量具备收敛保障的新算法。
原文摘要 · Abstract (English)
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.
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