Convergence Results for Inertial Regularized Bilevel Variational Inequality Problems
Date
2024
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
University of the Witwatersrand, Johannesburg
Abstract
In this dissertation, we introduce and study the inertial forward-reflected-backward method for approximating a solution of bilevel variational inequality problems. Our proposed method involves a single projection onto a feasible set, one functional evaluation and adopts the inertial extrapolation term. These features make our algorithm cost-effective and efficient, which is desirable when the cost operator and the feasible set have a complex structure. We incorporate the regularization technique in our method and establish that the sequences generated by our method converge strongly to a solution of the bilevel variational inequality problem studied in this work; furthermore, we modified our method by replacing the stepsizes and projection onto a feasible set with a self-adaptive
non-monotonic stepsizes and projection onto a constructive halfspace, respectively. The non-monotonic stepsizes ensure that our method performs without the previous detail of the Lipschitz constant, and the projection onto a constructive halfspace is cheap since its computation is through an explicit formula. These adjustments in our method ensure an improved performance, cheap computation and easy implementation of our method. We show the strong convergence result of the iterative sequences. Lastly, we give numerical experiments comparing the performance of the proposed methods with existing methods
Description
Dissertation submitted in fulfillment of the requirements for the degree of Master of Science, Faculty of Science, School of Mathematics The University of the Witwatersrand, Johannesburg, Johannesburg 2024
Keywords
Convergence Result, Inertial Regularized Bilevel Variational, UCTD
Citation
Okorie, Kalu Okam. (2024). Convergence Results for Inertial Regularized Bilevel Variational Inequality Problems [Master’s dissertation , University of the Witwatersrand, Johannesburg]. WireDSpace. https://hdl.handle.net/10539/42245