The University of Southampton
University of Southampton Institutional Repository

Modified inertial Tseng method for solving variational inclusion and fixed point problems on Hadamard manifolds

Modified inertial Tseng method for solving variational inclusion and fixed point problems on Hadamard manifolds
Modified inertial Tseng method for solving variational inclusion and fixed point problems on Hadamard manifolds

In this article, we introduce a forward–backward splitting method with a new step size rule for finding a singularity point of an inclusion problem which is defined by means of a sum of a single-valued vector field and a multi-valued vector field on a Hadamard manifold. Using a Mann, viscosity and an inertial extrapolation method, we establish a convergence result without prior knowledge of the Lipschitz constant of the underlying operator. We present some applications of our result to variational inequality problem. Finally, we present some numerical examples to demonstrate the numerical behavior of our proposed method. The result discuss in this article extends and complements many related results in the literature.

Hadamard manifold, Riemannian manifold, Variational inclusion problem, inertial Tseng method, monotone operator
0003-6811
Abass, H.A.
2647ac82-5bc5-4624-9726-46e40f07b071
Oyewole, O.K.
1636d2cf-02c7-4899-b2ba-848b6f0ab938
Jolaoso, L.O.
102467df-eae0-4692-8668-7f73e8e02546
Aremu, K.O.
7c8766e4-ec45-4093-baca-e79f01088056
Abass, H.A.
2647ac82-5bc5-4624-9726-46e40f07b071
Oyewole, O.K.
1636d2cf-02c7-4899-b2ba-848b6f0ab938
Jolaoso, L.O.
102467df-eae0-4692-8668-7f73e8e02546
Aremu, K.O.
7c8766e4-ec45-4093-baca-e79f01088056

Abass, H.A., Oyewole, O.K., Jolaoso, L.O. and Aremu, K.O. (2023) Modified inertial Tseng method for solving variational inclusion and fixed point problems on Hadamard manifolds. Applicable Analysis. (doi:10.1080/00036811.2023.2256357).

Record type: Article

Abstract

In this article, we introduce a forward–backward splitting method with a new step size rule for finding a singularity point of an inclusion problem which is defined by means of a sum of a single-valued vector field and a multi-valued vector field on a Hadamard manifold. Using a Mann, viscosity and an inertial extrapolation method, we establish a convergence result without prior knowledge of the Lipschitz constant of the underlying operator. We present some applications of our result to variational inequality problem. Finally, we present some numerical examples to demonstrate the numerical behavior of our proposed method. The result discuss in this article extends and complements many related results in the literature.

Text
Manifold 2 inclusion Rev - Accepted Manuscript
Download (456kB)

More information

Accepted/In Press date: 2 September 2023
e-pub ahead of print date: 11 September 2023
Published date: 11 September 2023
Additional Information: Publisher Copyright: © 2023 Informa UK Limited, trading as Taylor & Francis Group.
Keywords: Hadamard manifold, Riemannian manifold, Variational inclusion problem, inertial Tseng method, monotone operator

Identifiers

Local EPrints ID: 482709
URI: http://eprints.soton.ac.uk/id/eprint/482709
ISSN: 0003-6811
PURE UUID: d2b2992a-7528-4f92-9c23-e30086e96f8f
ORCID for L.O. Jolaoso: ORCID iD orcid.org/0000-0002-4838-7465

Catalogue record

Date deposited: 11 Oct 2023 16:55
Last modified: 11 Sep 2024 04:01

Export record

Altmetrics

Contributors

Author: H.A. Abass
Author: O.K. Oyewole
Author: L.O. Jolaoso ORCID iD
Author: K.O. Aremu

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×