# Online Primal-Dual Methods with Measurement Feedback for Time-Varying Convex Optimization

arXiv: https://arxiv.org/abs/1804.05159 · HTML: https://mlsanity.com/paper/1804.05159/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Apr 2018.

## Built on by (most cited first, 6 of 6)

- [Stochastic Saddle Point Problems with Decision-Dependent Distributions](https://mlsanity.com/paper/2201.02313/) (2022)
- [Stochastic Online Optimization for Cyber-Physical and Robotic Systems](https://mlsanity.com/paper/2404.05318/) (2024)
- [Prediction techniques for dynamic imaging with online primal-dual methods](https://mlsanity.com/paper/2405.02497/) (2024)
- [Online Convex Optimization and Integral Quadratic Constraints: An automated approach to regret analysis](https://mlsanity.com/paper/2503.23600/) (2025)
- [Augmented Lagrangian Methods for Time-varying Constrained Online Convex Optimization](https://mlsanity.com/paper/2205.09571/) (2022)
- [Online optimisation for dynamic electrical impedance tomography](https://mlsanity.com/paper/2412.12944/) (2024)

## Abstract (arXiv)

This paper addresses the design and analysis of feedback-based online algorithms to control systems or networked systems based on performance objectives and engineering constraints that may evolve over time. The emerging time-varying convex optimization formalism is leveraged to model optimal operational trajectories of the systems, as well as explicit local and network-level operational constraints. Departing from existing batch and feed-forward optimization approaches, the design of the algorithms capitalizes on an online implementation of primal-dual projected-gradient methods; the gradient steps are, however, suitably modified to accommodate feedback from the system in the form of measurements - hence, the term "online optimization with feedback." By virtue of this approach, the resultant algorithms can cope with model mismatches in the algebraic representation of the system states and outputs, they avoid pervasive measurements of exogenous inputs, and they naturally lend themselves to a distributed implementation. Under suitable assumptions, analytical convergence claims are established in terms of dynamic regret. Furthermore, when the synthesis of the feedback-based online algorithms is based on a regularized Lagrangian function, Q-linear convergence to solutions of the time-varying optimization problem is shown.