Abstract: In this talk, we introduce the dynamical system approach and Lyapunov analysis framework for linearly constrained convex optimization. Motivated by the primal-dual hybrid gradient (PDHG) method, a novel primal-dual flow model with biult-in time rescaling factor is firstly presented. Exponential decay of a proper Lyapunov function shall be established, and an equilibrium analysis shows the superiority over the classical saddle-point system. Then it is extended to a second-order model, called accelerated primal-dual flow, and an optimal first-order primal-dual method is proposed based on an implicit-explicit time discretization.