Abstract
We propose an inertial primal-dual dynamic with damping and scaling coefficients, which involves inertial terms both for primal and dual variables, for a linearly constrained convex optimization problem in a Hilbert setting. With different choices of damping and scaling coefficients, by a Lyapunov analysis approach, we investigate the asymptotic properties of the dynamic and prove its fast convergence results. Our results can be viewed as extensions of the existing ones on inertial dynamical systems for the unconstrained convex optimization problem to the primal-dual one for the linearly constrained convex optimization problem.
Acknowledgments
The authors would like to thank the referees and the editor for their helpful comments and suggestions which have led to the improvement of this paper.
Disclosure statement
No potential conflict of interest was reported by the authors.