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
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
11 September 2023
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).
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.
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Manifold 2 inclusion Rev
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Accepted/In Press date: 2 September 2023
e-pub ahead of print date: 11 September 2023
Published date: 11 September 2023
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© 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
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Date deposited: 11 Oct 2023 16:55
Last modified: 18 Mar 2024 04:04
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Contributors
Author:
H.A. Abass
Author:
O.K. Oyewole
Author:
K.O. Aremu
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