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Improved subgradient extragradient methods for solving pseudomonotone variational inequalities in Hilbert spaces

Improved subgradient extragradient methods for solving pseudomonotone variational inequalities in Hilbert spaces
Improved subgradient extragradient methods for solving pseudomonotone variational inequalities in Hilbert spaces
The purpose of this work to investigate pseudomonotone and Lipschitz continuous variational inequalities in real Hilbert spaces. For solving this problem, we propose two new methods which combine advantages of the subgradient extragradient method and the projection contraction method. Similar to some recent developments, the proposed methods do not require the knowledge of the Lipschitz constant associated with the variational inequality mapping. Under suitable mild conditions, we establish the weak and strong convergence of the proposed algorithms. Moreover, linear convergence is obtained under strong pseudomonotonicity and Lipschitz continuity assumptions. Numerical examples in fractional programming and optimal control problems demonstrate the potential of our algorithms as well as compare their performances to several related results.
Mann type method, Projection and contraction method, Pseudomonotone mapping, Subgradient extragradient method, Variational inequality problem
0168-9274
221-238
Thong, Duong Viet
645f66a1-787f-4e21-87b5-719f2fd987ae
Vuong, P. T.
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Thong, Duong Viet
645f66a1-787f-4e21-87b5-719f2fd987ae
Vuong, P. T.
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf

Thong, Duong Viet and Vuong, P. T. (2021) Improved subgradient extragradient methods for solving pseudomonotone variational inequalities in Hilbert spaces. Applied Numerical Mathematics, 163, 221-238. (doi:10.1016/j.apnum.2021.01.017).

Record type: Article

Abstract

The purpose of this work to investigate pseudomonotone and Lipschitz continuous variational inequalities in real Hilbert spaces. For solving this problem, we propose two new methods which combine advantages of the subgradient extragradient method and the projection contraction method. Similar to some recent developments, the proposed methods do not require the knowledge of the Lipschitz constant associated with the variational inequality mapping. Under suitable mild conditions, we establish the weak and strong convergence of the proposed algorithms. Moreover, linear convergence is obtained under strong pseudomonotonicity and Lipschitz continuity assumptions. Numerical examples in fractional programming and optimal control problems demonstrate the potential of our algorithms as well as compare their performances to several related results.

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TV_VIP_APNUM_R2 - Accepted Manuscript
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More information

Accepted/In Press date: 25 January 2021
e-pub ahead of print date: 28 January 2021
Published date: 1 May 2021
Keywords: Mann type method, Projection and contraction method, Pseudomonotone mapping, Subgradient extragradient method, Variational inequality problem

Identifiers

Local EPrints ID: 447119
URI: http://eprints.soton.ac.uk/id/eprint/447119
ISSN: 0168-9274
PURE UUID: 781e3f92-f62c-4155-8556-8477d75eaa44
ORCID for P. T. Vuong: ORCID iD orcid.org/0000-0002-1474-994X

Catalogue record

Date deposited: 03 Mar 2021 17:32
Last modified: 26 Nov 2021 03:20

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Contributors

Author: Duong Viet Thong
Author: P. T. Vuong ORCID iD

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