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arXiv · 1803.01825

On the Exponential Stability of Primal-Dual Gradient Dynamics

Guannan Qu·Na Li
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Abstract

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.

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Guannan Qu, Na Li. 2018-03-05. On the Exponential Stability of Primal-Dual Gradient Dynamics. https://doi.org/10.1109/lcsys.2018.2851375

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