A second-order dynamical system for equilibrium problems
A second-order dynamical system for equilibrium problems
We consider a second-order dynamical system for solving equilibrium problems in Hilbert spaces. Under mild conditions, we prove existence and uniqueness of strong global solution of the proposed dynamical system. We establish the exponential convergence of trajectories under strong pseudo-monotonicity and Lipschitz-type conditions. We then investigate a discrete version of the second-order dynamical system, which leads to a fixed point-type algorithm with inertial effect and relaxation. The linear convergence of this algorithm is established under suitable conditions on parameters. Finally, some numerical experiments are reported confirming the theoretical results.
Dynamic programming, Equilibrium problem, Exponential stability, Linear convergence, Lipschitz continuity, Monotonicity
327-351
Vinh, Le Van
4b6c0443-d29e-460c-9096-ff8795ba3b46
Tran, Van Nam
58f376d1-567a-4d75-a91c-4301850c57ba
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
September 2022
Vinh, Le Van
4b6c0443-d29e-460c-9096-ff8795ba3b46
Tran, Van Nam
58f376d1-567a-4d75-a91c-4301850c57ba
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Vinh, Le Van, Tran, Van Nam and Vuong, Phan Tu
(2022)
A second-order dynamical system for equilibrium problems.
Numerical Algorithms, 91 (1), .
(doi:10.1007/s11075-022-01264-4).
Abstract
We consider a second-order dynamical system for solving equilibrium problems in Hilbert spaces. Under mild conditions, we prove existence and uniqueness of strong global solution of the proposed dynamical system. We establish the exponential convergence of trajectories under strong pseudo-monotonicity and Lipschitz-type conditions. We then investigate a discrete version of the second-order dynamical system, which leads to a fixed point-type algorithm with inertial effect and relaxation. The linear convergence of this algorithm is established under suitable conditions on parameters. Finally, some numerical experiments are reported confirming the theoretical results.
Text
2ndOrder_DSEP_NUMA_Final
- Accepted Manuscript
More information
Accepted/In Press date: 21 January 2022
e-pub ahead of print date: 10 February 2022
Published date: September 2022
Additional Information:
Funding Information:
The authors are grateful to both anonymous referees for their constructive comments, which helped improve the presentation of this paper. The research of Le Van Vinh is funded by Van Lang University, Vietnam. Nam Van Tran thanks the support from Ho Chi Minh City University of Technology and Education.
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Keywords:
Dynamic programming, Equilibrium problem, Exponential stability, Linear convergence, Lipschitz continuity, Monotonicity
Identifiers
Local EPrints ID: 455039
URI: http://eprints.soton.ac.uk/id/eprint/455039
ISSN: 1017-1398
PURE UUID: e27309fa-2774-48ab-98cc-22c9a910751c
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Date deposited: 04 Mar 2022 17:40
Last modified: 17 Mar 2024 07:08
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Author:
Le Van Vinh
Author:
Van Nam Tran
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