  This paper develops a continuous-time primal-dual accelerated method with an
increasing damping coefficient for a class of convex optimization problems with
affine equality constraints. This paper analyzes critical values for parameters
in the proposed method and prove that the rate of convergence in terms of the
duality gap function is $O(\tfrac{1}{t^2})$ by choosing suitable parameters. As
far as we know, this is the first continuous-time primal-dual accelerated
method that can obtain the optimal rate. Then this work applies the proposed
method to two network optimization problems, a distributed optimization problem
with consensus constraints and a distributed extended monotropic optimization
problem, and obtains two variant distributed algorithms. Finally, numerical
simulations are given to demonstrate the efficacy of the proposed method.
