The Glowinski–Le Tallec splitting method revisited in the framework of equilibrium problems in Hilbert spaces
The Glowinski–Le Tallec splitting method revisited in the framework of equilibrium problems in Hilbert spaces
In this paper, we introduce a new approach for solving equilibrium problems in Hilbert spaces. First, we transform the equilibrium problem into the problem of finding a zero of a sum of two maximal monotone operators. Then, we solve the resulting problem using the Glowinski–Le Tallec splitting method and we obtain a linear rate of convergence depending on two parameters. In particular, we enlarge significantly the range of these parameters given rise to the convergence. We prove that the sequence generated by the new method converges to a global solution of the considered equilibrium problem. Finally, numerical tests are displayed to show the efficiency of the new approach.
477-495
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Strodiot, Jean Jacques
31543686-3a24-46f8-87f7-0c3af6b86c98
1 February 2018
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Strodiot, Jean Jacques
31543686-3a24-46f8-87f7-0c3af6b86c98
Vuong, Phan Tu and Strodiot, Jean Jacques
(2018)
The Glowinski–Le Tallec splitting method revisited in the framework of equilibrium problems in Hilbert spaces.
Journal of Global Optimization, 70 (2), .
(doi:10.1007/s10898-017-0575-0).
Abstract
In this paper, we introduce a new approach for solving equilibrium problems in Hilbert spaces. First, we transform the equilibrium problem into the problem of finding a zero of a sum of two maximal monotone operators. Then, we solve the resulting problem using the Glowinski–Le Tallec splitting method and we obtain a linear rate of convergence depending on two parameters. In particular, we enlarge significantly the range of these parameters given rise to the convergence. We prove that the sequence generated by the new method converges to a global solution of the considered equilibrium problem. Finally, numerical tests are displayed to show the efficiency of the new approach.
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Accepted/In Press date: 1 October 2017
e-pub ahead of print date: 9 October 2017
Published date: 1 February 2018
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Local EPrints ID: 434727
URI: http://eprints.soton.ac.uk/id/eprint/434727
ISSN: 0925-5001
PURE UUID: 6b7764a7-fa90-4c34-a8ad-f9a1e19bdfdf
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Date deposited: 07 Oct 2019 16:30
Last modified: 16 Mar 2024 04:42
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Author:
Jean Jacques Strodiot
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