@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.",
year = "2022",
doi = "10.1080/02331934.2021.1901289",
language = "English",
volume = "71",
pages = "3485--3514",
journal = "Optimization",
issn = "0233-1934",
publisher = "Taylor and Francis Ltd.",
number = "12",
}