Variational inequality over the set of common solutions of a system of bilevel variational inequality problem with applications

Eslamian, Mohammad

doi:10.1007/s13398-021-01193-2

Cited by 3 publications

(2 citation statements)

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“…Several mathematical problems, such as variational inequality problems, equilibrium problems, split feasibility problems, and split minimization problems, are all special MIP cases. These problems have been applied to solve diverse real-world problems, such as modeling inverse problems arising from phase retrieval, modeling intensity-modulated radiation therapy planning, sensor networks in computerized and data compression, optimal control problems, and image/signal processing problems [21][22][23].…”

Section: Introductionmentioning

confidence: 99%

“…The bilevel programming problem is a constrained optimization problem in which the constrained set is a solution set of another optimization problem. This problem is enriched with many applications in modeling Stackelberg games, the convex feasibility problem, determination in Wardrop equilibria for network flow, domain decomposition methods for PDEs, optimal control problems, and image/signal processing problems [23].…”

Section: Introductionmentioning

confidence: 99%

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On Bilevel Monotone Inclusion and Variational Inequality Problems

Ofem,

Abuchu,

Nabwey

et al. 2023

Mathematics

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In this article, the problem of solving a strongly monotone variational inequality problem over the solution set of a monotone inclusion problem in the setting of real Hilbert spaces is considered. To solve this problem, two methods, which are improvements and modifications of the Tseng splitting method, and projection and contraction methods, are presented. These methods are equipped with inertial terms to improve their speed of convergence. The strong convergence results of the suggested methods are proved under some standard assumptions on the control parameters. Also, strong convergence results are achieved without prior knowledge of the operator norm. Finally, the main results of this research are applied to solve bilevel variational inequality problems, convex minimization problems, and image recovery problems. Some numerical experiments to show the efficiency of our methods are conducted.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%