Publication Cover
Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 15
166
Views
3
CrossRef citations to date
0
Altmetric
Articles

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

ORCID Icon, &
Pages 4114-4139 | Received 13 Apr 2022, Accepted 15 Jul 2022, Published online: 26 Jul 2022
 

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.

AMS Classifications:

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].

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.