Exponential Stability of Primal-Dual Gradient Dynamics with Non-Strong Convexity Conference Paper uri icon

abstract

  • This paper studies the exponential stability of the primal-dual gradient dynamics (PDGD) for solving convex optimization problems where constraints are in the form of Ax + By = d and the objective is minx,y f (x) + g(y) with strongly convex smooth f but only convex smooth g. We show that when g is a quadratic function or when g and matrix B together satisfy an inequality condition, the PDGD can achieve global exponential stability given that matrix A is of full row rank. These results indicate that the PDGD is locally exponentially stable with respect to any convex smooth g under a regularity condition. Two quadratic Lyapunov functions are designed to prove the exponential stability. Lastly, numerical experiments further complement the theoretical analysis.

name of conference

  • 2020 American Control Conference (ACC)

published proceedings

  • 2020 American Control Conference (ACC)

author list (cited authors)

  • Chen, X., & Li, N. a.

citation count

  • 13

complete list of authors

  • Chen, Xin||Li, Na

publication date

  • July 2020