A refined convergence analysis of Popov's algorithm for pseudo-monotone variational inequalities
A refined convergence analysis of Popov's algorithm for pseudo-monotone variational inequalities
In this work, we present a refined convergence analysis of the Popov's projection algorithm for solving pseudo-monotone variational inequalities in Hilbert spaces. Our analysis results in a larger range of stepsize, which is achieved by using a new Lyapunov function. Furthermore, when the operator is strongly pseudo-monotone and Lipschitz continuous, we establish the linear convergence of the sequence generated by the Popov's algorithm. As a by-product of our analysis, we extend the range of stepsize in the projected reflected gradient algorithm for solving unconstrained pseudo-monotone variational inequalities.
Popov's projection algorithm, Variational inequality, linear convergence, pseudo monotonicity
Hai, Le Thi Thanh
c3f40bd6-2358-4612-b9c1-44c8a986b18b
Trinh, Thanh Quoc
a0abb7a5-96af-42c8-987e-da1c7a2daa2c
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
11 August 2023
Hai, Le Thi Thanh
c3f40bd6-2358-4612-b9c1-44c8a986b18b
Trinh, Thanh Quoc
a0abb7a5-96af-42c8-987e-da1c7a2daa2c
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Hai, Le Thi Thanh, Trinh, Thanh Quoc and Vuong, Phan Tu
(2023)
A refined convergence analysis of Popov's algorithm for pseudo-monotone variational inequalities.
Optimization.
(doi:10.1080/02331934.2023.2245414).
Abstract
In this work, we present a refined convergence analysis of the Popov's projection algorithm for solving pseudo-monotone variational inequalities in Hilbert spaces. Our analysis results in a larger range of stepsize, which is achieved by using a new Lyapunov function. Furthermore, when the operator is strongly pseudo-monotone and Lipschitz continuous, we establish the linear convergence of the sequence generated by the Popov's algorithm. As a by-product of our analysis, we extend the range of stepsize in the projected reflected gradient algorithm for solving unconstrained pseudo-monotone variational inequalities.
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Accepted/In Press date: 26 July 2023
e-pub ahead of print date: 11 August 2023
Published date: 11 August 2023
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© 2023 Informa UK Limited, trading as Taylor & Francis Group.
Keywords:
Popov's projection algorithm, Variational inequality, linear convergence, pseudo monotonicity
Identifiers
Local EPrints ID: 481796
URI: http://eprints.soton.ac.uk/id/eprint/481796
ISSN: 0233-1934
PURE UUID: 9520a7cb-dfb0-4e46-880b-225671f03268
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Date deposited: 08 Sep 2023 16:31
Last modified: 18 Mar 2024 03:54
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Author:
Le Thi Thanh Hai
Author:
Thanh Quoc Trinh
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