Current browse context:
math
Change to browse by:
References & Citations
Mathematics > Optimization and Control
Title: A Framework for Time-Varying Optimization via Derivative Estimation
(Submitted on 28 Mar 2024)
Abstract: 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.
Link back to: arXiv, form interface, contact.