2024/11/28 by Umberto Casti, Casti, Umberto, Sandro Zampieri +1 · 3 citations
Computer Science · #FOS: Electrical engineering #FOS: Mathematics #Mobile and Web Applications #Optimization and Control (math.OC) #Optimization and Search Problems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2411.19056
openalex publication_date 2024/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we propose control-theoretic methods as tools for the design of online optimization algorithms that are able to address dynamic, noisy, and partially uncertain time-varying quadratic objective functions. Our approach introduces two algorithms specifically tailored for scenarios where the cost function follows a stochastic linear model. The first algorithm is based on a Kalman filter-inspired approach, leveraging state estimation techniques to account for the presence of noise in the evolution of the objective function. The second algorithm applies H_∞-robust control strategies to enhance performance under uncertainty, particularly in cases in which model parameters are characterized by a high variability. Through numerical experiments, we demonstrate that our algorithms offer significant performance advantages over the traditional gradient-based method and also over the optimization strategy proposed in arXiv:2205.13932 based on deterministic models.