Year: 2024
Type: preprint
Abstract: We propose an adaptive method for online time-varying (TV) convex optimization, termed $\mathcal{L}_{1}$ adaptive optimization ($\mathcal{L}_{1}$-AO). TV optimizers utilize a prediction model to exploit the temporal structure of TV problems, which can be inaccurate in the online implementation. Inspired by $\mathcal{L}_{1}$ adaptive control, the proposed method augments an adaptive update law to estimate and compensate for the uncertainty from the prediction inaccuracies. The proposed method provides performance bounds of the error in the optimization variables and cost function, allowing efficient and reliable optimization for TV problems. Numerical simulation results demonstrate the effectiveness of the proposed method for online TV convex optimization.
Source: arXiv (Cornell University)
Authors: Kim, Jinrae, Hovakimyan, Naira
Institution: University of Illinois Urbana-Champaign
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403784003