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A second order dynamical system and its discretization for strongly pseudo-monotone variational inequalities

A second order dynamical system and its discretization for strongly pseudo-monotone variational inequalities
A second order dynamical system and its discretization for strongly pseudo-monotone variational inequalities
We consider a second order dynamical system for solving variational inequalities in Hilbert spaces. Under standard conditions, we prove the existence and uniqueness of strong global solution of the proposed dynamical system. The exponential convergence of trajectories is established under strong pseudo-monotonicity and Lipschitz continuity assumptions. A discrete version of the proposed dynamical system leads to a relaxed inertial projection algorithm whose linear convergence is proved under suitable conditions on parameters. We discuss the possibility of extension to general monotone inclusion problems. Finally some numerical experiments are reported demonstrating the theoretical results.


Dynamical system, Exponential convergence, Linear convergence, Monotone inclusion, Strong pseudo-monotonicity, Variational inequality
2875–2897
Vuong, Phan T
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Vuong, Phan T
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf

Vuong, Phan T (2021) A second order dynamical system and its discretization for strongly pseudo-monotone variational inequalities. SIAM Journal of Control and Optimization, 59 (4), 2875–2897. (doi:10.1137/20M1335297).

Record type: Article

Abstract

We consider a second order dynamical system for solving variational inequalities in Hilbert spaces. Under standard conditions, we prove the existence and uniqueness of strong global solution of the proposed dynamical system. The exponential convergence of trajectories is established under strong pseudo-monotonicity and Lipschitz continuity assumptions. A discrete version of the proposed dynamical system leads to a relaxed inertial projection algorithm whose linear convergence is proved under suitable conditions on parameters. We discuss the possibility of extension to general monotone inclusion problems. Finally some numerical experiments are reported demonstrating the theoretical results.


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Accepted/In Press date: 30 March 2021
e-pub ahead of print date: 9 August 2021
Published date: 9 August 2021
Keywords: Dynamical system, Exponential convergence, Linear convergence, Monotone inclusion, Strong pseudo-monotonicity, Variational inequality

Identifiers

Local EPrints ID: 450880
URI: http://eprints.soton.ac.uk/id/eprint/450880
PURE UUID: 9dd0ddfe-b0d5-42b9-90c1-f9b1a72f01be
ORCID for Phan T Vuong: ORCID iD orcid.org/0000-0002-1474-994X

Catalogue record

Date deposited: 18 Aug 2021 16:30
Last modified: 26 Nov 2021 03:20

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