Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems

Bing Tan (), Xiaolong Qin () and Jen-Chih Yao ()
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Bing Tan: University of Electronic Science and Technology of China
Xiaolong Qin: Hangzhou Normal University
Jen-Chih Yao: China Medical University

Journal of Global Optimization, 2022, vol. 82, issue 3, No 5, 523-557

Abstract: Abstract This paper investigates some inertial projection and contraction methods for solving pseudomonotone variational inequality problems in real Hilbert spaces. The algorithms use a new non-monotonic step size so that they can work without the prior knowledge of the Lipschitz constant of the operator. Strong convergence theorems of the suggested algorithms are obtained under some suitable conditions. Some numerical experiments in finite- and infinite-dimensional spaces and applications in optimal control problems are implemented to demonstrate the performance of the suggested schemes and we also compare them with several related results.

Keywords: Variational inequality problem; Projection and contraction method; Subgradient extragradient method; Inertial method; Pseudomonotone mapping; Optimal control problem; 47H05; 47H09; 49J15; 47J20; 65K15 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10898-021-01095-y

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