# Online Proximal-ADMM For Time-varying Constrained Convex Optimization

arXiv: https://arxiv.org/abs/2005.03267 · HTML: https://mlsanity.com/paper/2005.03267/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 May 2020.

## Built on by (most cited first, 10 of 10)

- [Stochastic Saddle Point Problems with Decision-Dependent Distributions](https://mlsanity.com/paper/2201.02313/) (2022)
- [Peer-to-Peer Energy Trading of Solar and Energy Storage: A Networked Multiagent Reinforcement Learning Approach](https://mlsanity.com/paper/2401.13947/) (2024)
- [Prediction techniques for dynamic imaging with online primal-dual methods](https://mlsanity.com/paper/2405.02497/) (2024)
- [WEEP: A Differentiable Nonconvex Sparse Regularizer via Weakly-Convex Envelope](https://mlsanity.com/paper/2507.20447/) (2025)
- [Augmented Lagrangian Methods for Time-varying Constrained Online Convex Optimization](https://mlsanity.com/paper/2205.09571/) (2022)
- [Multivariate regression modeling in integrative analysis via sparse regularization](https://mlsanity.com/paper/2304.07451/) (2023)
- [Online Non-Stationary Stochastic Quasar-Convex Optimization](https://mlsanity.com/paper/2407.03601/) (2024)
- [Online optimisation for dynamic electrical impedance tomography](https://mlsanity.com/paper/2412.12944/) (2024)
- [Structure-Dependent Regret and Constraint Violation Bounds for Online Convex Optimization with Time-Varying Constraints](https://mlsanity.com/paper/2603.14319/) (2026)
- [Information Bottleneck under Perfect Privacy](https://mlsanity.com/paper/2608.11003/) (2026)

## Abstract (arXiv)

This paper considers a convex optimization problem with cost and constraints that evolve over time. The function to be minimized is strongly convex and possibly non-differentiable, and variables are coupled through linear constraints. In this setting, the paper proposes an online algorithm based on the alternating direction method of multipliers (ADMM), to track the optimal solution trajectory of the time-varying problem; in particular, the proposed algorithm consists of a primal proximal gradient descent step and an appropriately perturbed dual ascent step. The paper derives tracking results, asymptotic bounds, and linear convergence results. The proposed algorithm is then specialized to a multi-area power grid optimization problem, and our numerical results verify the desired properties.