Inertial primal-dual dynamics with damping and scaling for linearly constrained convex optimization problems

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.

Keywords:

• Inertial primal-dual dynamical system
• linearly constrained convex optimization problem
• damping and scaling
• Lyapunov analysis approach
• convergence rate

AMS Classifications:

• 34D05
• 37N40
• 46N10
• 90C25

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.

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China [grant number 11471230].