# On the Exponential Stability of Primal-Dual Gradient Dynamics

arXiv: https://arxiv.org/abs/1803.01825 · HTML: https://mlsanity.com/paper/1803.01825/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Mar 2018.

## Built on by (most cited first, 12 of 12)

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- [Convex Q Learning in a Stochastic Environment: Extended Version](https://mlsanity.com/paper/2309.05105/) (2023)
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- [A primal-dual perspective for distributed TD-learning](https://mlsanity.com/paper/2310.00638/) (2023)
- [Analysis of Off-Policy Multi-Step TD-Learning with Linear Function Approximation](https://mlsanity.com/paper/2402.15781/) (2024)
- [Fixed-Time Convergence for a Class of Nonconvex-Nonconcave Min-Max Problems](https://mlsanity.com/paper/2207.12845/) (2022)
- [Stability of Primal-Dual Gradient Flow Dynamics for Multi-Block Convex Optimization Problems](https://mlsanity.com/paper/2408.15969/) (2024)
- [From exponential to finite/fixed-time stability: Applications to optimization](https://mlsanity.com/paper/2409.11713/) (2024)
- [Contractivity and linear convergence in bilinear saddle-point problems: An operator-theoretic approach](https://mlsanity.com/paper/2410.14592/) (2024)
- [R-GTD: A Geometric Analysis of Gradient Temporal-Difference Learning in Singular Regimes](https://mlsanity.com/paper/2601.20599/) (2026)
- [Constrained Flow Matching via Lagrangian Dual Flows](https://mlsanity.com/paper/2607.04513/) (2026)
- [Equilibrium bias and convergence in augmented primal--dual dynamics with sampled constraints](https://mlsanity.com/paper/2609.13925/) (2026)

## Abstract (arXiv)

Continuous time primal-dual gradient dynamics that find a saddle point of a Lagrangian of an optimization problem have been widely used in systems and control. While the global asymptotic stability of such dynamics has been well-studied, it is less studied whether they are globally exponentially stable. In this paper, we study the primal-dual gradient dynamics for convex optimization with strongly-convex and smooth objectives and affine equality or inequality constraints, and prove global exponential stability for such dynamics. Bounds on decaying rates are provided.