# A Passivity-Based Method for Accelerated Convex Optimisation

arXiv: https://arxiv.org/abs/2306.11474 · HTML: https://mlsanity.com/paper/2306.11474/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 12 references that are in the map.
- First posted on arXiv 20 Jun 2023.

## Builds on (most cited first, 6 of 6)

- [A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights](https://mlsanity.com/paper/1503.01243/) (2015)
- [Dissipativity Theory for Nesterov's Accelerated Method](https://mlsanity.com/paper/1706.04381/) (2017)
- [Control Interpretations for First-Order Optimization Methods](https://mlsanity.com/paper/1703.01670/) (2017)
- [The Analysis of Optimization Algorithms, A Dissipativity Approach](https://mlsanity.com/paper/2205.14264/) (2022)
- [Continuous-Time Analysis of Accelerated Gradient Methods via Conservation Laws in Dilated Coordinate Systems](https://mlsanity.com/paper/2202.05501/) (2022)
- [Inducing Uniform Asymptotic Stability in Non-Autonomous Accelerated Optimization Dynamics via Hybrid Regularization](https://mlsanity.com/paper/1905.12110/) (2019)

## Abstract (arXiv)

This study presents a constructive methodology for designing accelerated convex optimisation algorithms in continuous-time domain. The two key enablers are the classical concept of passivity in control theory and the time-dependent change of variables that maps the output of the internal dynamic system to the optimisation variables. The Lyapunov function associated with the optimisation dynamics is obtained as a natural consequence of specifying the internal dynamics that drives the state evolution as a passive linear time-invariant system. The passivity-based methodology provides a general framework that has the flexibility to generate convex optimisation algorithms with the guarantee of different convergence rate bounds on the objective function value. The same principle applies to the design of online parameter update algorithms for adaptive control by re-defining the output of internal dynamics to allow for the feedback interconnection with tracking error dynamics.