A new projection-type method with nondecreasing adaptive step-sizes for pseudo-monotone Variational Inequalities
A new projection-type method with nondecreasing adaptive step-sizes for pseudo-monotone Variational Inequalities
We propose a new projection-type method with inertial extrapolation for solving pseudo-monotone and Lipschitz continuous variational inequalities in Hilbert spaces. The proposed method does not require the knowledge of the Lipschitz constant as well as the sequential weak continuity of the corresponding operator. We introduce a self-adaptive procedure, which generates dynamic step-sizes converging to a positive constant. It is proved that the sequence generated by the proposed method converges weakly to a solution of the considered variational inequality with the nonasymptotic O(1/n) convergence rate. Moreover, the linear convergence is established under strong pseudo-monotonicity and Lipschitz continuity assumptions. Numerical a exmples for solving a class of Nash–Cournot oligopolistic market equilibrium model and a network equilibrium flow problem are given illustrating the efficiency of the proposed method.
Convergence rate, Lipschitz continuity, Pseudo-monotonicity, Variational inequality
803-829
Thong, Duong Viet
645f66a1-787f-4e21-87b5-719f2fd987ae
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Anh, Pham Ky
ecffe94c-2596-4512-8c17-e0e1e2d26e5a
Muu, Le Dung
78e28849-0beb-44ba-9a47-35d47390985a
December 2022
Thong, Duong Viet
645f66a1-787f-4e21-87b5-719f2fd987ae
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Anh, Pham Ky
ecffe94c-2596-4512-8c17-e0e1e2d26e5a
Muu, Le Dung
78e28849-0beb-44ba-9a47-35d47390985a
Thong, Duong Viet, Vuong, Phan Tu, Anh, Pham Ky and Muu, Le Dung
(2022)
A new projection-type method with nondecreasing adaptive step-sizes for pseudo-monotone Variational Inequalities.
Networks and Spatial Economics, 22 (4), .
(doi:10.1007/s11067-022-09568-7).
Abstract
We propose a new projection-type method with inertial extrapolation for solving pseudo-monotone and Lipschitz continuous variational inequalities in Hilbert spaces. The proposed method does not require the knowledge of the Lipschitz constant as well as the sequential weak continuity of the corresponding operator. We introduce a self-adaptive procedure, which generates dynamic step-sizes converging to a positive constant. It is proved that the sequence generated by the proposed method converges weakly to a solution of the considered variational inequality with the nonasymptotic O(1/n) convergence rate. Moreover, the linear convergence is established under strong pseudo-monotonicity and Lipschitz continuity assumptions. Numerical a exmples for solving a class of Nash–Cournot oligopolistic market equilibrium model and a network equilibrium flow problem are given illustrating the efficiency of the proposed method.
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More information
Accepted/In Press date: 9 May 2022
e-pub ahead of print date: 25 June 2022
Published date: December 2022
Additional Information:
Funding Information:
The authors are grateful to the Editors and the anonymous referees for their constructive comments, which helped improve the presentation of this paper.
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Keywords:
Convergence rate, Lipschitz continuity, Pseudo-monotonicity, Variational inequality
Identifiers
Local EPrints ID: 467497
URI: http://eprints.soton.ac.uk/id/eprint/467497
ISSN: 1566-113X
PURE UUID: f1360bc5-2911-4438-809c-38d641db57a9
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Date deposited: 11 Jul 2022 17:04
Last modified: 17 Mar 2024 07:25
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Author:
Duong Viet Thong
Author:
Pham Ky Anh
Author:
Le Dung Muu
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