# Optimization Algorithms as Robust Feedback Controllers

arXiv: https://arxiv.org/abs/2103.11329 · HTML: https://mlsanity.com/paper/2103.11329/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2021.

## Built on by (most cited first, 9 of 9)

- [Towards a Systems Theory of Algorithms](https://mlsanity.com/paper/2401.14029/) (2024)
- [Learning to optimize with convergence guarantees using nonlinear system theory](https://mlsanity.com/paper/2403.09389/) (2024)
- [Decision-Dependent Stochastic Optimization: The Role of Distribution Dynamics](https://mlsanity.com/paper/2503.07324/) (2025)
- [M-HOF-Opt: Multi-Objective Hierarchical Output Feedback Optimization via Multiplier Induced Loss Landscape Scheduling](https://mlsanity.com/paper/2403.13728/) (2024)
- [The Artificial Neural Twin -- Process Optimization and Continual Learning in Distributed Process Chains](https://mlsanity.com/paper/2403.18343/) (2024)
- [Markovian Foundations for Quasi-Stochastic Approximation in Two Timescales: Extended Version](https://mlsanity.com/paper/2409.07842/) (2024)
- [An Improved FOX Optimization Algorithm Using Adaptive Exploration and Exploitation for Global Optimization](https://mlsanity.com/paper/2504.09574/) (2025)
- [A Control-Barrier-Function-Based Algorithm for Policy Adaptation in Reinforcement Learning](https://mlsanity.com/paper/2510.02720/) (2025)
- [OpenG2G: A Simulation Platform for AI Datacenter-Grid Runtime Coordination](https://mlsanity.com/paper/2605.05519/) (2026)

## Abstract (arXiv)

Mathematical optimization is one of the cornerstones of modern engineering research and practice. Yet, throughout all application domains, mathematical optimization is, for the most part, considered to be a numerical discipline. Optimization problems are formulated to be solved numerically with specific algorithms running on microprocessors. An emerging alternative is to view optimization algorithms as dynamical systems. Besides being insightful in itself, this perspective liberates optimization methods from specific numerical and algorithmic aspects and opens up new possibilities to endow complex real-world systems with sophisticated self-optimizing behavior. Towards this goal, it is necessary to understand how numerical optimization algorithms can be converted into feedback controllers to enable robust "closed-loop optimization". In this article, we focus on recent control designs under the name of "feedback-based optimization" which implement optimization algorithms directly in closed loop with physical systems. In addition to a brief overview of selected continuous-time dynamical systems for optimization, our particular emphasis in this survey lies on closed-loop stability as well as the robust enforcement of physical and operational constraints in closed-loop implementations. To bypass accessing partial model information of physical systems, we further elaborate on fully data-driven and model-free operations. We highlight an emerging application in autonomous reserve dispatch in power systems, where the theory has transitioned to practice by now. We also provide short expository reviews of pioneering applications in communication networks and electricity grids, as well as related research streams, including extremum seeking and pertinent methods from model predictive and process control, to facilitate high-level comparisons with the main topic of this survey.