An inertial projection and contraction method with a line search technique for variational inequality and fixed point problems
Lateef Olakunle Jolaoso*
In this paper, we study the approximation of common elements in the set of solutions of a variational inequality problem with monotone and Lipschitz continuous operator and the set of fixed points of a relatively nonexpansive mapping in real Hilbert space. We introduce an inertial projection and contraction method with a line search technique for solving the considered problem. A strong convergence result is proved without any prior estimate of the Lipschitz constant of the variational inequality operator. Furthermore, we provide some numerical experiments using performance profile metrics and application to image deblurring problem to illustrate the efficiency and accuracy of our algorithm.
Banach spaces
Variational inequalities
extragradient method
line search
monotone operator
projection and contraction
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Contraction Method Mathematics 100%
Projection Method Business & Economics 98%
Hilbert spaces Engineering & Materials Science 90%
Variational Inequalities Business & Economics 86%
Fixed Point Business & Economics 84%
Line Search Mathematics 75%
Contraction Business & Economics 70%
Jolaoso, L. O. (2022). An inertial projection and contraction method with a line search technique for variational inequality and fixed point problems. Optimization, 71(12), 3485-3514. https://doi.org/10.1080/02331934.2021.1901289
Jolaoso, Lateef Olakunle. / An inertial projection and contraction method with a line search technique for variational inequality and fixed point problems. In: Optimization. 2022 ; Vol. 71, No. 12. pp. 3485-3514.
@article{1839c7bc8d564823b0f90c4ddb1e57d8,
title = "An inertial projection and contraction method with a line search technique for variational inequality and fixed point problems",
abstract = "In this paper, we study the approximation of common elements in the set of solutions of a variational inequality problem with monotone and Lipschitz continuous operator and the set of fixed points of a relatively nonexpansive mapping in real Hilbert space. We introduce an inertial projection and contraction method with a line search technique for solving the considered problem. A strong convergence result is proved without any prior estimate of the Lipschitz constant of the variational inequality operator. Furthermore, we provide some numerical experiments using performance profile metrics and application to image deblurring problem to illustrate the efficiency and accuracy of our algorithm.",
keywords = "Banach spaces, Variational inequalities, extragradient method, line search, monotone operator, projection and contraction",
author = "Jolaoso, {Lateef Olakunle}",
note = "Funding Information: The author sincerely thank the editor and anonymous referees for the careful reading, constructive comments and fruitful suggestions that substantially improved the manuscript. The author acknowledge with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University for making their facilities available for the research. This research is supported by the postdoctoral research fund at the Sefako Makgatho Health Science University, Pretoria, South Africa. Funding Information: The author sincerely thank the editor and anonymous referees for the careful reading, constructive comments and fruitful suggestions that substantially improved the manuscript. The author acknowledge with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University for making their facilities available for the research. This research is supported by the postdoctoral research fund at the Sefako Makgatho Health Science University, Pretoria, South Africa. Publisher Copyright: {\textcopyright} 2021 Informa UK Limited, trading as Taylor & Francis Group.",
journal = "Optimization",
Jolaoso, LO 2022, 'An inertial projection and contraction method with a line search technique for variational inequality and fixed point problems', Optimization, vol. 71, no. 12, pp. 3485-3514. https://doi.org/10.1080/02331934.2021.1901289
An inertial projection and contraction method with a line search technique for variational inequality and fixed point problems. / Jolaoso, Lateef Olakunle.
In: Optimization, Vol. 71, No. 12, 2022, p. 3485-3514.
T1 - An inertial projection and contraction method with a line search technique for variational inequality and fixed point problems
N1 - Funding Information: The author sincerely thank the editor and anonymous referees for the careful reading, constructive comments and fruitful suggestions that substantially improved the manuscript. The author acknowledge with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University for making their facilities available for the research. This research is supported by the postdoctoral research fund at the Sefako Makgatho Health Science University, Pretoria, South Africa. Funding Information: The author sincerely thank the editor and anonymous referees for the careful reading, constructive comments and fruitful suggestions that substantially improved the manuscript. The author acknowledge with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University for making their facilities available for the research. This research is supported by the postdoctoral research fund at the Sefako Makgatho Health Science University, Pretoria, South Africa. Publisher Copyright: © 2021 Informa UK Limited, trading as Taylor & Francis Group.
N2 - In this paper, we study the approximation of common elements in the set of solutions of a variational inequality problem with monotone and Lipschitz continuous operator and the set of fixed points of a relatively nonexpansive mapping in real Hilbert space. We introduce an inertial projection and contraction method with a line search technique for solving the considered problem. A strong convergence result is proved without any prior estimate of the Lipschitz constant of the variational inequality operator. Furthermore, we provide some numerical experiments using performance profile metrics and application to image deblurring problem to illustrate the efficiency and accuracy of our algorithm.
AB - In this paper, we study the approximation of common elements in the set of solutions of a variational inequality problem with monotone and Lipschitz continuous operator and the set of fixed points of a relatively nonexpansive mapping in real Hilbert space. We introduce an inertial projection and contraction method with a line search technique for solving the considered problem. A strong convergence result is proved without any prior estimate of the Lipschitz constant of the variational inequality operator. Furthermore, we provide some numerical experiments using performance profile metrics and application to image deblurring problem to illustrate the efficiency and accuracy of our algorithm.
KW - Banach spaces
KW - Variational inequalities
KW - extragradient method
KW - line search
KW - monotone operator
KW - projection and contraction
JO - Optimization
JF - Optimization
Jolaoso LO. An inertial projection and contraction method with a line search technique for variational inequality and fixed point problems. Optimization. 2022;71(12):3485-3514. doi: 10.1080/02331934.2021.1901289