A Framework for Time-Varying Optimization via Derivative Estimation
<|reference_start|>A Framework for Time-Varying Optimization via Derivative Estimation: Optimization algorithms have a rich and fundamental relationship with ordinary differential equations given by its continuous-time limit. When the cost function varies with time -- typically in response to a dynamically changing environment -- online optimization becomes a continuous-time trajectory tracking problem. To accommodate these time variations, one typically requires some inherent knowledge about their nature such as a time derivative.   In this paper, we propose a novel construction and analysis of a continuous-time derivative estimation scheme based on "dirty-derivatives", and show how it naturally interfaces with continuous-time optimization algorithms using the language of ISS (Input-to-State Stability). More generally, we show how a simple Lyapunov redesign technique leads to provable suboptimality guarantees when composing this estimator with any well-behaved optimization algorithm for time-varying costs.<|reference_end|>
@article{marchi2024a,
    title={A Framework for Time-Varying Optimization via Derivative Estimation},
    author={Matteo Marchi, Jonathan Bunton, Jo~ao Pedro Silvestre, Paulo Tabuada},
    journal={arXiv preprint arXiv:2403.19088},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.19088},
    primaryClass={math.OC cs.SY eess.SY}
}