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The Forward-Backward-Forward Method from continuous and discrete perspective for pseudo-monotone variational inequalities in Hilbert spaces

The Forward-Backward-Forward Method from continuous and discrete perspective for pseudo-monotone variational inequalities in Hilbert spaces
The Forward-Backward-Forward Method from continuous and discrete perspective for pseudo-monotone variational inequalities in Hilbert spaces
Tseng’s forward-backward-forward algorithm is a valuable alternative for Korpelevich’s extragradient method when solving variational inequalities over a convex and closed set governed by monotone and Lipschitz continuous operators, as it requires in every step only one projection operation. However, it is well-known that Korpelevich’s method converges and can therefore be used also for solving variational inequalities governed by pseudo-monotone and Lipschitz continuous operators. In this paper, we first associate to a pseudo-monotone variational inequality a forward-backward-forward dynamical system and carry out an asymptotic analysis for the generated trajectories. The explicit time discretization of this system results into Tseng’s forward-backward-forward algorithm with relaxation parameters, which we prove to converge also when it is applied to pseudo-monotone variational inequalities. In addition, we show that linear convergence is guaranteed under strong pseudo-monotonicity. Numerical experiments are carried out for pseudo-monotone variational inequalities over polyhedral sets and fractional programming problems.
Convex programming, Dynamical system, Pseudo-monotonicity, Tseng's FBF algorithm, Variational inequalities
0377-2217
49-60
Bot, Radu Ioan
d4eaeb1e-c774-4c45-a273-b078e66b2af7
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Csetnek, E.R.
064ece98-12e2-4f61-99cf-cd30fd20dbbf
Bot, Radu Ioan
d4eaeb1e-c774-4c45-a273-b078e66b2af7
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Csetnek, E.R.
064ece98-12e2-4f61-99cf-cd30fd20dbbf

Bot, Radu Ioan, Vuong, Phan Tu and Csetnek, E.R. (2020) The Forward-Backward-Forward Method from continuous and discrete perspective for pseudo-monotone variational inequalities in Hilbert spaces. European Journal of Operational Research, 287 (1), 49-60. (doi:10.1016/j.ejor.2020.04.035).

Record type: Article

Abstract

Tseng’s forward-backward-forward algorithm is a valuable alternative for Korpelevich’s extragradient method when solving variational inequalities over a convex and closed set governed by monotone and Lipschitz continuous operators, as it requires in every step only one projection operation. However, it is well-known that Korpelevich’s method converges and can therefore be used also for solving variational inequalities governed by pseudo-monotone and Lipschitz continuous operators. In this paper, we first associate to a pseudo-monotone variational inequality a forward-backward-forward dynamical system and carry out an asymptotic analysis for the generated trajectories. The explicit time discretization of this system results into Tseng’s forward-backward-forward algorithm with relaxation parameters, which we prove to converge also when it is applied to pseudo-monotone variational inequalities. In addition, we show that linear convergence is guaranteed under strong pseudo-monotonicity. Numerical experiments are carried out for pseudo-monotone variational inequalities over polyhedral sets and fractional programming problems.

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1-s2.0-S037722172030388X-main - Accepted Manuscript
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More information

Accepted/In Press date: 17 April 2020
e-pub ahead of print date: 28 April 2020
Published date: 16 November 2020
Keywords: Convex programming, Dynamical system, Pseudo-monotonicity, Tseng's FBF algorithm, Variational inequalities

Identifiers

Local EPrints ID: 439623
URI: http://eprints.soton.ac.uk/id/eprint/439623
ISSN: 0377-2217
PURE UUID: 4ac4833f-b60c-4b6f-9587-1ebf79a474c5
ORCID for Phan Tu Vuong: ORCID iD orcid.org/0000-0002-1474-994X

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Date deposited: 28 Apr 2020 16:35
Last modified: 28 Apr 2022 04:53

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Contributors

Author: Radu Ioan Bot
Author: Phan Tu Vuong ORCID iD
Author: E.R. Csetnek

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