A dynamical system for strongly pseudo-monotone equilibrium problems
A dynamical system for strongly pseudo-monotone equilibrium problems
In this paper, we consider a dynamical system for solving equilibrium problems in the framework of Hilbert spaces. First, we prove that under strong pseudo-monotonicity and Lipschitz-type continuity assumptions, the dynamical system has a unique equilibrium solution, which is also globally exponentially stable. Then, we derive the linear rate of convergence of a discrete version of the proposed dynamical system to the unique solution of the problem. Global error bounds are also provided to estimate the distance between any trajectory and this unique solution. Some numerical experiments are reported to confirm the theoretical results.
Dynamical system, Equilibrium problem, Error bound, Global exponential stability, Strong pseudo-monotonicity
767-784
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Strodiot, Jean Jacques
13ab7e92-c999-4be9-90c0-f81a7f372459
June 2020
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Strodiot, Jean Jacques
13ab7e92-c999-4be9-90c0-f81a7f372459
Vuong, Phan Tu and Strodiot, Jean Jacques
(2020)
A dynamical system for strongly pseudo-monotone equilibrium problems.
Journal of Optimization Theory and Applications, 185 (3), .
(doi:10.1007/s10957-020-01669-y).
Abstract
In this paper, we consider a dynamical system for solving equilibrium problems in the framework of Hilbert spaces. First, we prove that under strong pseudo-monotonicity and Lipschitz-type continuity assumptions, the dynamical system has a unique equilibrium solution, which is also globally exponentially stable. Then, we derive the linear rate of convergence of a discrete version of the proposed dynamical system to the unique solution of the problem. Global error bounds are also provided to estimate the distance between any trajectory and this unique solution. Some numerical experiments are reported to confirm the theoretical results.
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Vuong-Strodiot A Dynamical System For EP JOTA 2020
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Accepted/In Press date: 21 April 2020
e-pub ahead of print date: 20 May 2020
Published date: June 2020
Keywords:
Dynamical system, Equilibrium problem, Error bound, Global exponential stability, Strong pseudo-monotonicity
Identifiers
Local EPrints ID: 441007
URI: http://eprints.soton.ac.uk/id/eprint/441007
ISSN: 0022-3239
PURE UUID: 3daab5d5-97b6-4252-a4fb-7fc83cf3370e
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Date deposited: 27 May 2020 16:53
Last modified: 17 Mar 2024 03:58
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Author:
Jean Jacques Strodiot
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