CMI Seminar: Guannan Qu
Exponential stability of primal-dual gradient dynamics and its applications in network control
Primal-dual gradient dynamics (PDGD) that find a saddle point of a Lagrangian of an optimization problem have been widely used in systems and control. In these applications, it is important for such dynamics to have strong stability guarantees, like global exponential stability. However, while the global asymptotic stability of PDGD has been well-studied, it is less studied whether PDGD is globally exponentially stable.
In this talk, we study the primal-dual gradient dynamics for constrained convex optimization and provide conditions that guarantee its global exponential stability. We also present its applications in a smart grid control problem.