# Semi-Global Exponential Stability of Augmented Primal-Dual Gradient Dynamics for Constrained Convex Optimization

arXiv: https://arxiv.org/abs/1903.09580 · HTML: https://mlsanity.com/paper/1903.09580/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Mar 2019.

## Built on by (most cited first, 4 of 4)

- [Convergence Rates of Two-Time-Scale Gradient Descent-Ascent Dynamics for Solving Nonconvex Min-Max Problems](https://mlsanity.com/paper/2112.09579/) (2021)
- [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)
- [Equilibrium bias and convergence in augmented primal--dual dynamics with sampled constraints](https://mlsanity.com/paper/2609.13925/) (2026)

## Abstract (arXiv)

Primal-dual gradient dynamics that find saddle points of a Lagrangian have been widely employed for handling constrained optimization problems. Building on existing methods, we extend the augmented primal-dual gradient dynamics (Aug-PDGD) to incorporate general convex and nonlinear inequality constraints, and we establish its semi-global exponential stability when the objective function is strongly convex. We also provide an example of a strongly convex quadratic program of which the Aug-PDGD fails to achieve global exponential stability. Numerical simulation also suggests that the exponential convergence rate could depend on the initial distance to the KKT point.