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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
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
0233-1934
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
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).

Record type: Article

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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POPOV_VIP_GOPT_accepted - Accepted Manuscript
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More information

Accepted/In Press date: 26 July 2023
e-pub ahead of print date: 11 August 2023
Published date: 11 August 2023
Additional Information: Publisher Copyright: © 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
ORCID for Phan Tu Vuong: ORCID iD orcid.org/0000-0002-1474-994X

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Date deposited: 08 Sep 2023 16:31
Last modified: 26 Jul 2024 04:01

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Contributors

Author: Le Thi Thanh Hai
Author: Thanh Quoc Trinh
Author: Phan Tu Vuong ORCID iD

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