An extragradient-type method for solving nonmonotone quasi-equilibrium problems
An extragradient-type method for solving nonmonotone quasi-equilibrium problems
In this paper, a quasi-equilibrium problem with a nonmonotone bifunction is considered in a finite-dimensional space. The primary difficulty with this problem is related to the fact that one must simultaneously solve a nonmonotone equilibrium problem and calculate a fixed point of a multivalued mapping. An extragradient-type method is presented and analysed for its solution. The convergence of the method is proved under the assumption that the solution set of an associated dual equilibrium problem is nonempty. Finally, some numerical experiments are reported.
651-664
Van, N. T. T.
c6042e3d-4cf8-4419-80c8-925768fac27f
Strodiot, J. J.
dd5fc8de-1a1f-4128-a0ea-7403f2699f48
Nguyen, V. H.
a83b9c2e-8544-454c-a397-97c178160ecd
Vuong, P. T.
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
4 May 2018
Van, N. T. T.
c6042e3d-4cf8-4419-80c8-925768fac27f
Strodiot, J. J.
dd5fc8de-1a1f-4128-a0ea-7403f2699f48
Nguyen, V. H.
a83b9c2e-8544-454c-a397-97c178160ecd
Vuong, P. T.
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Van, N. T. T., Strodiot, J. J., Nguyen, V. H. and Vuong, P. T.
(2018)
An extragradient-type method for solving nonmonotone quasi-equilibrium problems.
Optimization, 67 (5), .
(doi:10.1080/02331934.2017.1416610).
Abstract
In this paper, a quasi-equilibrium problem with a nonmonotone bifunction is considered in a finite-dimensional space. The primary difficulty with this problem is related to the fact that one must simultaneously solve a nonmonotone equilibrium problem and calculate a fixed point of a multivalued mapping. An extragradient-type method is presented and analysed for its solution. The convergence of the method is proved under the assumption that the solution set of an associated dual equilibrium problem is nonempty. Finally, some numerical experiments are reported.
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Accepted/In Press date: 7 December 2017
e-pub ahead of print date: 21 December 2017
Published date: 4 May 2018
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Local EPrints ID: 435038
URI: http://eprints.soton.ac.uk/id/eprint/435038
ISSN: 0233-1934
PURE UUID: 51db957e-a745-49b4-8215-160cde563bf4
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Date deposited: 18 Oct 2019 16:30
Last modified: 16 Mar 2024 04:42
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Author:
N. T. T. Van
Author:
J. J. Strodiot
Author:
V. H. Nguyen
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