# The Analysis of Optimization Algorithms, A Dissipativity Approach

arXiv: https://arxiv.org/abs/2205.14264 · HTML: https://mlsanity.com/paper/2205.14264/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 May 2022.

## Built on by (most cited first, 5 of 5)

- [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)
- [Convergence of energy-based learning in linear resistive networks](https://mlsanity.com/paper/2503.00349/) (2025)
- [A Passivity-Based Method for Accelerated Convex Optimisation](https://mlsanity.com/paper/2306.11474/) (2023)
- [Generalization as a robust performance property of learning-enabled dynamical systems](https://mlsanity.com/paper/2608.30431/) (2026)

## Abstract (arXiv)

Optimization problems in engineering and applied mathematics are typically solved in an iterative fashion, by systematically adjusting the variables of interest until an adequate solution is found. The iterative algorithms that govern these systematic adjustments can be viewed as a control system. In control systems, the output in measured and the input is adjusted using feedback to drive the error to zero. Similarly, in iterative algorithms, the optimization objective is evaluated and the candidate solution is adjusted to drive it toward the optimal point. Choosing an algorithm that works well for a variety of optimization problems is akin to robust controller design. Just as dissipativity theory can be used to analyze the stability properties of control systems, it can also be used to analyze the convergence properties of iterative algorithms. By defining an appropriate notion of "energy" that dissipates with every iteration of the algorithm, the convergence properties of the algorithm can be characterized. This article formalizes the connection between iterative algorithms and control systems and shows through examples how dissipativity theory can be used to analyze the performance of many classes of optimization algorithms. This control-theoretic viewpoint enables the selection and tuning of optimization algorithms to be performed in an automated and systematic way.